First New Bit...

In finest bottom up design methods, I'm starting at the end and working my way forwards. The nicely rendered bit above is the output shaft for the reversing box. It'll sit coaxially with the input shaft (hence the big hole in the middle) and can be driven two ways. The first (and most common) way will be for dogs to engage in the slots on the front and drive the output shaft directly. These dogs will be on a sliding collar splined to the input shaft. In this fashion there will be a non-geared direct connection between engine and output shaft.

The second way will be for a gear to turn the output shaft. If we take the drive from the input shaft via a pair of gears to a layshaft and then via two extra gears to the gear on the output shaft then we'll reverse the direction of travel of the output shaft relative to the input shaft and hey presto - reverse gear. Now given that bike engines tend to major more on power (by virtue of stratospheric rev limits) than torque, a degree of speed reduction (and hence torque multiplication) might well be a good thing as the driver won't need to necessarily slip the clutch mightily to get the thing moving in reverse.

Now for all this to work with a minimum of nasty mechanical graunching noises, all the gears will have to be in constant mesh. This will mean that the gear on the input shaft must float and only be connected when we want reverse gear. If we use the other end of the sliding collar to do the connect then we have a workable design. Everything else is metallurgy and calculations...

Oops...

I know it's been a bit of a while but somebody pressed my 'get a life' button again and I've changed jobs (while still teaching as well) and a home (re)construction project has been filling what is euphemistically termed spare time. Never mind, I'm back now and I suppose I had better get on with some non-paying real work.

One of the requirements for RGB racers is a working reverse system, something that the majority of bikes (and all bikes if you don't class a Honda Goldwing as a motorcycle) don't seem to have fitted. If you've gone for a longitudinal installation of your engine then it's relatively easy to have an extra gearbox between output cog and differential. Unfortunately, I seem to have plumped for a mid-engine layout which makes for a much simpler differential layout (using chain and sprockets just like the donor bike) but does hamper the ability to go backwards under the influence of the engine. A lot of racers use a second starter motor acting on the drive chain but these seem to have a relatively large failure rate (and failure when tested is an automatic disqualification) not to mention issues with how the torque is delivered. The fact that I'm a mechanical engineer rather than an electron herder seems to be pushing me down a purely mechanical option.

So knocking out a quick specification for a black box, I get the following list of desirable features:

1. Lightweight and compact
   
2. User switchable between forward and reverse
3. Minimal transmission losses in forward mode

And that's about it... I'm still at the brain storming stage but I can envisage a system that is basically the reverse gear and top gear from an old gearbox. With one of these you have direct drive from input to output in forward mode and a small geartrain in reverse.

Adjustment...

Sorry there's not been a post for a little while but life has been a little frantic around here, with a mixture of the start of term (my beloved leader is currently tearing his hair out as we've got about 50% more students than we needed/wanted/expected) and the need to rebuild our outhouse before it collapsed taking the house with it. Even worse than that, I haven't got a SolidWorks model to throw up as a picture. Normal service will be resumed soon.

Anyway, getting back on track, I want to make my suspension design adjustable for two reasons: firstly, I have no doubts that any chassis that gets manufactured is going to have dimensional accuracies measurable by thumb widths and the suspension will need to be tweaked back so that it matches what was originally designed. I have a friend who makes recycling lorries for a living and he works to plus or minus 5mm. Secondly, you will want to fiddle with camber and caster settings to get the right grip balance for corners (why you'd want to tweak them will come later when I do the spring rates).

The classic way of performing suspension adjustments is to screw your balljoints (If you're in a cheap formula) or Rose/Heim joints (as stolen from the Luftwaffe at the end of World War II and gifted to either of those two fine engineering companies - one UK and one US) if you're working with cash. If you happen to follow Formula SAE, you'll now that one thing that makes judges tear their hair out is the REIB problem - 'rod end in bending'. Formula SAE goes for light weight - very light, as any car over 200 kg doesn't get through to design finals - which means that the rod ends would look ridiculously tiny on remote control cars. If the rod end isn't fully screwed home the stresses on it cause horrendous distortion and early failure.

I'm unlikely to be using 6mm joints on any design soon, so we can simply spec up the joints to account for any excess bending - in effect over-engineering the joint. If it does bend, it's probably better that it deforms rather than the suspension arms or, god forbid, the chassis. Rod ends are relatively cheap (and as an aside, don't engineer anything in brass for the foreseeable future - I've just ordered a load for the workshop and it's twice the price of Aluminium) and more importantly, easy to replace.

By screwing the joint in or out we can effectively change the length of a suspension are and thus the camber angle of the wheel. If we just have a simple threaded suspension arm, we have to dismantle the suspension to adjust it. This is not a trivial exercise, and more importantly it at least quadruples the effort required to get a car squared away as you have to go through vast cycles of disassembly-adjustment-reassembly-measure to get the numbers you're looking for. Many cars have adjustment ladders - effectively a turnbuckle with a left hand thread at one end and a right hand thread at the other. These add to the length of the arm, and more importantly add extra weight as you have to over engineer to potential joints in bending.

There is another option - a coaxial turnbuckle (I promise to forget about students tomorrow and CAD one up for your general delectation). All the threads are co-axial so adjustment is made by turning the middle portion. Clever thinking also tells you that you can play silly buggers with the thread pitches to give yourself significantly finer adjustment than a normal fine pitch thread.

As for caster, I considered all the sane and insane options and decided to go with having spacers on the inner mounting arms and thus the ability to shift arms longitudinally to angle the upright. SusProg suggests that I'll need around 20mm of movement in the top arm to get 7.5 degrees of caster. Any more than that and the driver will need to go to the gym a lot to be able to turn the wheel accurately - even with the low weight.

Making sense of the Regulations...

Now, I know that I'm supposed to make sense of regulations, or at least try and find all the useful loopholes in them, but the RACMSA 'Blue Book' makes about as much sense as a bucket of chocolate frogs. I'm trying to work out how small I can make the tubing for the spaceframe chassis, and depending on which interpretation of the rules you like. Section Q covers all the safety features you could or should fit on a car and paragraph 1.3 mandates CDS steel tubing, with a minimum yield strength of 350 MPa and either 45x2.5 mm or 50x2mm diameter and wall thicknesses. Yet paragraph 1.5.2 for Sports racing cars says a minimum of 48.3mm with a wall thickness of 2.6mm and 1.5.4 (b) for non-standard cars says 32x1.5mm. Which is right? I think we should be a Sports racing car rather than a 'non-standard' car, but there are significant weight penalties for using thicker than necessary tubing.

So if we look at the cross-sectional areas of the four options we get values of 333mm², 301mm², 373mm² and 143mm². The maximum compressive force that these members can take before starting to permanently deform (for those who remember A-level physics, the equation is of course Force = Stress x Area), varies between 50 kN for the lowest member and 130kN for the largest area. So which is adequate and which will give you a few short microseconds of terror before a basilar skull fracture puts you out of your misery for good?

The human resistance to acceleration was found out in nicely empirical fashion by Dr John Stapp of the USAF who strapped himself to a rocket sled and pulled 46.2G in a frontal deceleration. Using Newton's second law (Force = Mass x Acceleration), if we get our car down to the minimum weight of 560kg, we get an impact force of 254 kN. If that impact force is suddenly applied (and you can bet it is), the initial impact stress is actually double that (so effectively we can only use half the limiting impact force if we want no margin of safety). I'm vastly oversimplifying the reality, but SolidWorks doesn't come with a copy of DYNA3D or PAMCRASH, which is what the automotive industry use for this sort of thing.

Anyway, if we have two roll hoops, with extra front and rear stays, we'll have 8 struts resisting an impact force.
If we use the smallest diameter tubing the cage will yield under such loading, whereas if we use the largest tubing we have a factor of safety of around 2. Is it really worth saving weight if you get one of those once in a lifetime accidents - and you want to be around to tell the grandchildren all about it? I'd be inclined to use the lightest of the large tubing (which has other advantages, such as being less likely to buckle than the thinner diameter - so that's 50mmx2mm thickness round tubing.

For frontal impacts we can trade deformation for force - i.e. limiting the force and hoping the car stops before the metal tubing makes contact with our delicate feet. F1 expects a peak rate of deceleration of 10g for the first 150mm of deformation, and 20g for the first 60kJ or energy absorption. For our car 20g and assuming that our non-CDS metal tubing (so a yield strength that could be as low as 275 MPa) will yield under such an impact, we need an impact force of 110 kN and thus a cross sectional area of about 400mm². There will probably be 4 frontal force members here (and a nice big chuck of energy absorbing honeycomb to keep the force at those levels for at least the initial phase of the impact). So each tube needs a cross-sectional area of 100mm². So it's a case of running through the sizes to work out what tubing will work in these areas. A quick bit of maths lets me know that I need tubing that weighs around 780 g/m. In circular tubing that means 7/8"x16g, in square that means ¾"x16g and in rectangular we can use 1"x½"x16g.

I finally got out to measure someone's chassis and bodywork at the weekend and the picture at the top is a quick revision of the chassis, less the back end and using thinner tubing. With a 50mm diameter cage on the top, but using only ½" round tubing, the whole lot weighs around 34kg. The chassis was using 1" tubing and had a lot of extra tubes knocking around (it was originally a prototype chassis), so weighed considerably more. Even with a ramping up in tube size, I reckon we can get significant weight savings in place to get the car close to (or even below) minimum weight.

Safety

Now no racer would ever imagine that they're going to have a really BIG accident, and certainly one where they impact the rollbar at a really nasty angle. I spent the thick end of a decade investigating RTAs and I've seen the impossible happen quite a lot. So, I wanted to see what my allegedly natty rollbar design really would do in the event of a shunt. I've loaded the top part of the rollbar with 10kN (effectively a tonne) and at the same time applied the same level of force horizontally - sort of landing upside-down while sliding into a brickwall with just the rollbar taking the loading. This is nowhere near as sever as F1 for example, which expects loading of 90kN through the rollover structure.

With this loading the rollbar only just survives - the factor of safety, i.e. the ratio between yield stress and max stress, is 0.97 so some parts of the rollbar would just start to bend. Dynamic crush testing is way beyond my knowledge of Cosmos, but I'm more certain than ever that I'll want either front stays on that roll bar or a full roll cage tying the rollbar to another roll hoop around the steering wheel area. Once I've got the rest of the chassis, I'll repeat the analysis and see what the whole car will do. I'll also see if I can get some dynamic analysis done using Cosmos.

The other thing I want to do is have sensible impact protection to the front and sides. Aluminium honeycomb is your friend here and I've got both Hexcel's design document and the F1 regulations as an input value:

"For the purposes of this test, the total weight of the trolley and test structure shall be 780kg and the velocity of impact 15.0 metres/sec.The resistance of the test structure must be such that during theimpact:
- the peak deceleration over the first 150mm of deformation does not exceed 10g;
- the peak deceleration over the first 60kJ energy absorption does not exceed 20g ;
- the average deceleration of the trolley does not exceed 40g ;
- the peak deceleration in the chest of the dummy does not exceed 60g for more than a cumulative 3ms, this being the resultant of data from three axes.
Furthermore, there must be no damage to the survival cell or to the mountings of the safety belts or fire extinguishers."

There's similar for side impact as well. I'll see what sort of volume of expanded honeycomb is required and see where it can be fitted in. I've seen some nasty intrusions into spaceframe chassis over the years and it's a risk I'd like to design out as much as possible.

Making progress...

As promised, I've got back onto SusProg to work out important things like position of pullrods, spring rates and the like. First problem was that pull rods simply weren't going to work as a triggering mechanism. Where I've put in the zero roll suspension there was effectively bugger all motion translated from the pullrod into the monoshock assembly to get any meaningful translation of a coil spring. This is not a good thing. I actually want the suspension to move, and more importantly, move under control and 10 mm of spring travel could be taken up by stiction, clerances and poor manufacturing.

So, pushrods it is, albeit at the expense of a little increase in centre of gravity height. That said, SolidWorks is reporting that the current unit is around 10kg, so I'm not unduly concerned with that minor growth. I used SusProg to work out suitable spring rates. I've gone for a ride frequency of 2 Hz which requires a spring rate of 310 lbf/in in this instance. 2 Hz is about the upper limit for ride frequency until you start getting ridiculous amounts of downforce, and I'll probably stiffen up the rear ride frequency by around 10% more. That can wait until I've actually got some ballpark weights to play with, rather than the 'pick a number out of the technical regulations and use that' option.

The picture at the top shows the layout of the front suspension in SusProg. SusProg can't actually calculate values for a monoshock, so it's really two separate bellcranks with coincidental spring and damper units. Still, it looks pretty and gives me some values, which is all-important. The key value is that for 50mm of bump and droop travel, I actually need around 85mm of damper travel, so the 40mm travel damper I've been playing with will need to be replaced. Creating a new damper is not of itself a major issue as all I have to do is change one number in Solidworks, but I now have the lead on issues of changing everything else to fit the central guide rail. The only ray of light is that the equivalent suspension travel in roll is going to be about an inch either way, so I'll be able to keep the guides very short and limit the bending moments on the shafts.

So, I've pretty much got the front sorted out now and we can think about putting the chassis together. Unlike certain 3D solid modellers, SolidWorks has a built-in facility for 'weldments'. That's spaceframes made out of random tubes to you and me. You simply have a separate drawing of the tube profile and a 3d wireframe sketch of where the tubes have to go, marry the two together and you get something like this:


You can even add mounting plates, weld fillets (there's a few on the drawing where I've joined said plates to the tube) and trim tubes so they don't appear inside each other. All-in-all, something pretty much designed to make a chassis designer's life easier. Of course until I measure the bodywork, I can't really put a design together, but that mockup meets the MSA requirements and weighs 12.3 kg. The basic concept for the chassis is to use that heavy rollbar to link into the engine mounts at the front and the differential and suspension pickup points at the rear to reduce weight as much as humanlymachinely possible. While I'm waiting to go and measure (work is intervening for the rest of this week), I'll get the modal suspension finished off...

More integration...

and a lazy way to do calculations. The Educational edition of Solidworks has the full-on CosmosWorks designer built in to it, and FloWorks, but I'm fairly sure I don't have enough processor cycles in my PC to sanely do any meaningful CFD studies. I thought I'd check out the possibility of integrating the body-side mounting of the heave spring into the big lump of metal that slides from side-to-side when the car rolls. A quick analysis later (and it took less than a minute to cue it up and run it - far, far better than when I used to use FEA in the days before Pentiums - I first used PAFEC on a Vax and IBM CAD on a mainframe) and you get the picture above. This is the von Mises plot, which is effectively a combinational stress criteria for yield (if you get yield when you combine the stresses in all three dimensions using the von mises formula, it'll probably yield in real life) when 5000N (a bit more than 500 kg) of loading is applied to the bolt hole. If you click on the drawing you'll get a better view, but the safety factor (i.e. the ratio of actual stress to peak stress) is just over three, so even if shock loading was applied, you'd still not cause that lump of metal to yield.

So, knowing that I'm not overloading the lump in question, I can clean the design up a bit, which gives the picture you see below:


I've shortened the guide rails as much as possible (I'll be running the geometry again to see what motion ratios I have and how much roll travel I actually need) to limit the bending moment on them and put a simple framework around that can be bolted onto the chassis in the most appropriate place. I'm now almost ready to start designing the chassis. Adrian has offered to let me measure his bodywork, so I know what space I have to play around with, and I've got a copy of the Blue Book to tell me what I can and can't do, so I'll start with the rollbar and go on from there.

Coming Together...

OK, the picture above is the central gubbins of the modal isolation suspension system. You have a central block which carries a normal coil spring on one side and a coil-over unit on the other. For the purposes of mock-up, I've modelled a Sachs Race Engineering damper, although at the eye-watering costs of these units, I can't imagine I'd ever actually use one. This central unit slides left-to-right on linear bearings (You could probably get away with plain bushes, but I'd want as little stiction in my suspension linkages as I can get away with, hence the posh guide bearings) when the car rolls. The big bearings at the bottom of the picture are to support a bell-crank that will rotate around the lower guide rail to give displacement control in bump. At the moment these are standard roller bearings, although it'll make more sense for them to be tapered to allow for the axial loads as the roll displacement works.

The only outstanding issue is to work out the sort of springs rates needed for this unit and to find someone prepared to do a 1:1 bump:rebound damper. Because of the mounting angle, we need a mono-shock damper and it's pretty rare to get a 1:1 ration for rebound forces as you normally want softer bump (which controls the wheel mass relative to the body) than rebound (which controls the body relative to the wheel mass). If it proves to be completely unfeasable (unlikely), there's nothing stopping you using two coil-over units mounted back to back across the central bar.

Update
I've put the bellcrank (I haven't put the bolt holes for location the two pull/push rods yet) in position with a second coil-over unit to show the heave spring mechanism as well. I was originally planning to attach the heave unit to the body directly and put some sort of guide bush in to deal with the side-to-side movement, but it seems possible to locate it onto the same central bracket that holds the roll coil-over. The only issue is that you want the guide rails then to be as short as possible to manage the bending loads they'll be undergoing as a result. If the loading all looks a little severe then I can still attach the heave coil-over to the body, I'll just have to tweak the mountings so there's sufficient articulation in the bushes.

Time to hit the calculator and work out if the attractive looking method will work...

Monoshocks and modal isolation...

Running on from yesterday's slightly cryptic post about modal isolation and the joy of being able to get exactly the right amount of damping in particular modes (getting the right amount of spring stiffness is usually easy). I thought I'd better elaborate. The picture above is from a Force hillclimb chassis (you can tell it's a hillclimber by the absence of just about everything in the search for stuff-all weight) and is about the best photograph I could find of a monoshock suspension. You can see that the two pushrods operate a single bellcrank. When both pushrods are displaced upwards, the crank rotates and moves the coilover unit in bump. When there is differential movement, the crank displaces along its 'axle' against the action of stacks of Belleville washers.

The design shown has two major design issues. There's very little roll movement possible and that movement is undamped. This isn't an issue in a wing-equipped car because you actually want very little roll else your expensive carbon fibre is going to be none-to-gently abrading itself on the tarmac. The absence of damping is an issue. At the end of the day these cars are going to be driven by amateur racers (gifted or not) and it's worth trading a few tenths of a second for driver confidence in the car. A car vibrating around in roll does not normally give a driver confidence.

So, how can we get around these two problems. Firstly we can replace the Belleville stack with normal helical coil springs. With more movement we can get more roll at less loading. With more lateral movement comes more side loading of the coilover unit which is bad, but this is easily curable by using a wider yoke rather than a clevis connect the coilover to the bellcrank. The only way to introduce damping is to fit a damper unit for the lateral movement. I'm thinking of having a Y-shaped bellcrank with a secondary inner arm. This inner arm would be static relative to the rotation of the bellcrank and move linearly with the roll movement. You can then fit a damper to the inner arm, connect it to the body and hey presto, properly damped, modally isolated suspension. and with little weight penalty over conventional two coilovers plus anti-roll bar.

The only other thing I'm considering is to put all this gubbins on the floor of the chassis and operate it by pullrods rather than push rods. A saving in centre of gravity height. In fact the only downside I can see is that corner weighting will be slightly harder as you'll have to preload one side of the roll springs relative to the other to transfer the weight. You do however get very easy ride height adjustment.

So I have a mental picture of how it'll all go together (I don't do visuals except in CAD becuase I'm quite possibly the World's worst sketch artist. I've got to sketch up a couple of dampers and some linear shaft bearings (well I say sketch, when I really mean drag them off of 3dContentCentral - thank you OnDrive) and then I can do a concept model for your general delectation.

Modal Isolation

Sorry for the absence of a post yesterday, but I was flat out on the CAD preparing for my evening class. They're going to be making a pipe vice, a mill stop and a plumb bob (or at least parts of them) as assessed pieces, so they all have to be modelled in CAD and then dimensioned up as 2D drawings before being cross referenced to the specifications of the qualification units. Anyway, here's a couple of quick renders of the two main items:
But getting back on with the car, I've been thinking long and hard about modal isolation, mainly because this month's issue of Racecar Engineering has a review of the Formula SAE/Student/FISITA World Cup events - annual competitions for university undergraduates to build their own deathtraps 600cc racing cars. Back when I was just a sprog in ride and handling terms, I worked closely with a certain British sports car manufacturer on fitting an active suspension system to a tank. The system worked on the principle of modal isolation. In other words instead of each wheel station having a spring and damper rate associated with it the overal vehicle was considered to have four specific spring and damper rates: roll, pitch, heave and warp. Warp was effectively torsion of the chassis, but that's probably better known to racecar engineers as either Roll Moment Distribution (if you read Milliken & Milliken) or Magic Number (If you've been trained by Claude Rouelle). Sitting in a car with a laptop you could change any of these rates and make either a dream handling vehicle or one that would disappear off into the undergrowth at the prod of a key. In fact if you had a half-decent egotist test driver you'd prod the key mid corner while trying desperately not to laugh as you sailed off into the undergrowth.


So, where does this come in for us - I'm hardly likely to specify an active ride system (especially as they cost around £500k - Moog servovalves tend to be around 10K each and you need at least eight per car). Well, on most cars the spring and damper units have to do all the work for all four modes and as a result you tend to have a bit of a pigs breakfast when it comes to getting an optimum solution, especially in damping of modes other than wheel heave. If you could have separate springs and dampers for everything, you could make large gains in handling without compromise.


Such systems are fairly popular on racecars - F3 have been using monoshock systems for over a decade, although these don't have any roll damping whatsoever. I'd be looking for a system that replaces the two coilover units and an antiroll bar with a pair of coilover units and a set of linkages and bellcranks. I've got a couple of ideas that I need to get modelled up so I can check the kinematics with Solidworks. I would ordinarily start designing my own rotary roll damper but I reckon that would be overkill so an extra bellcrank might be the order of the day. The basic idea is to have no ride springs and a T-type anti-roll bar connected between a pair of bellcranks operated by pushrods (or pullrods, for the benefit of my other reader). A coilover unit would be connected between the chassis and the centre of the T-type bar and thus be operated in heave. A second damper would be connected between a floating frame on the anti roll bar and the bar itself to give separate roll damping. It's the latter part that's causing some grief at the moment, mainly because the whole application lends itself wonderfully to rotary damping but chucks up a load of interesting kinematics problems when it comes to linear dampers.

Oh well, time to get the back of the fag packet out and start sketching...

Something other than cars...

I'm running an evening class for wannabe machinists, starting in September. One of the would-be master craftsmen asked a question about Stirling engines, which then segued into the little beast shown above (click on the picture for a larger view). For those who know their Stirling engines, it's a 'Ringbom' type that uses air pressure to move air between the hot and cold sides of the displacer rather than running the two pistons off a common crank arrangement.

Actually, it's probably a little complex to use for assessment pieces (not least because it's only around two inches high) - the qualification is at 'level 2' which is sort of equivalent to GCSE. That said, I'm hoping there'll be plenty of time available during the year and we can build one anyway. If we do, I'll re-engineer it (lets just say the person who designed it doesn't expect anyone trying to make it to have access to CNC machinery) for quicker manufacture.

Now back on with the car. I'm debating whether to install the spherical rod ends for the uprights in a pseudo-vertical or a pseudo-horizontal plane (by which I mean the axis of the hole). If I install them vertically, I'll have no issues with steering lock, but I might have articulation issues under bump. For a horizontal installation, it's vice-versa. I've been using the Aurora Bearings catalogue to try and make my choice and their rod ends would have around 35 degrees of articulation. If you look at yesterday's picture, you'll see that the joints are already relatively inclined, so I might have issues with wheel travel. I doubt that I'd need to use 35 degrees of articulation with turning. The tightest bend I know (the hairpin at Mallory) needs around 10 degrees of steering lock at the wheels to negotiate for a neutral steered car, which leaves plenty in reserve. I'll do some calculations and let you know the results.

Back to Geometry

With the information garnered from the upright model, I've been able to return to SusProg and try and finalise the suspension geometry, so that I can then engineer the chassis hardpoints and then get on with the design of the chassis itself. The picture above shows the (theoretical) final positions for the suspension arms, together with the best location for the steering rack to give minimal bump steer. For those who want a feel for the scale of the drawing, the thicker grid lines are 200mm apart and you're looking rearwards from the front centreline of the car.

I've rolled and bumped the suspension and got some feel for the geometry. As expected, there's very little change in roll centre height during roll, something of the order of 0.08 degrees inward for both wheels at 2 degrees of body roll. As I've said earlier, the net result of putting the instant centre on the centreline of the car is that you get a relatively shorter equivalent swing arm length (695mm in this case) compared to having less inclined suspension arms. According to SusProg, at 40 mm of bump travel, there's 3.5 degrees of negative camber. The roll centre doesn't move at all during roll, and is fixed at 132 mm above the ground.

Using SusProg to do all the hard maths for me has resulted in a total bump steer of 0.15mm toe-in at 100 mm bump, and around 10 microns over the range of +/-40mm wheel travel from static. One thing that I havn't considered up to now is the amount of Ackerman that the car will have. Ackerman is the method by which the inside wheel turns more than the outside when cornering. It's especially useful on circuits with tight corners, such as the hairpin at Mallory Park. At the moment the tie rod end is effectively outboard of the virtual kingpin, so the car has anti-Ackerman (277% for those who like meaningless numbers) and the outside wheel turns more. If I had sensible tyre data, I could actually work out if this was a bad thing or not. I don't and I doubt anyone will give me £200,000 to do some testing at CALSPAN, so I'll put it in the 'to be determined' pile for now. It's not an enormous issue, as I can do the same job on the steering arm as I did with the top rose joint mounting to offset it inward. In fact doing it that way would enable a range of Ackerman to be easily engineered and you could have a different geometry for Mallory than for Thruxton or Silverstone.

All done for now...

I think the upright is finished. One side effect of building the upright in two main parts, which I'd forgotten, is that there is no need to have two separate designs for nearside and offside. Those of you who look carefully at the finished design will spot the method for joining the two bits together. The aim is to mill a round-ended slot in the upright and have an identical mortice in the top extension. Ideally this will be a light interference fit (one of the joys of CNC is that you can do this sort of thing without the need for extensive grinding) which is further located by a pair of dowel pins for added strength. The cutaway below shows the joint a little better:



According to SolidWorks, that complete assembly weighs around 4 kg (and in reality probably less because the calliper has more volume than the real-life item. That's not too shabby, especially since the FEA results are looking fairly reasonable. I'm tempted to use a bit more mass and reinforce the upright slightly by reducing the size of the central hole in the purple bit. Now all that's together I can hit SusProg and get on with firming up the suspension geometry. After that should come the suspension hardpoints on the chassis and the chassis itself.

Back on track...

OK, 24 hours later and things are looking a bit better. I've changed the design for the upright by rotating the mounting holes through 45 degrees and then sending spurs off in the right direction for the various attachments. I've also come to a decision about manufacturing. While the idea of machining the whole thing out of solid billet has great appeal, the inward spur on the upright for the top wishbone mounting is going to be the thick end of 80-100mm inside the rest of the upright. This means that were this to be made out of billet around 85% of the billet would be converted into swarf. It seems to make a lot more sense to have a multi-part upright so that anyone with a milling machine can make the bits cheaply. I need to do some analysis on the loadings but I imagine that a properly designed joint is going to be no weaker than the billet method, and will be quicker and easier to manufacture, and cheaper to boot.

I decided to extend the method to the brake calliper mounting as well, as you can see in the complete assembled upright. This has the added side effect that other callipers can be easily accommodated for the unit without having to design and build new uprights every time. Now everything fits together and doesn't clash. I just need to do some FEA work to make sure the upright is meaty enough (the Mk I eyeball says it is, but I want to see what sort of safety margin I have when I've got 1.5g of cornering acceleration, a bit of downforce and 1.5g of braking applied too) and isn't going to fail like a US road bridge at the first sign of abuse.


Once I've satisfied myself with that, the I can get back to SusProg and finish the front suspension geometry off. I definitely want the zero camber change in roll, combined with zero bump steer (SusProg can calculate the position for the steering rack for me to achieve this)

Reasons not to be cheerful...

part one! Following on from the stress-free design of the front hub unit yesterday, I cracked on with the design of the upright that's going to glue all those miscellaneous parts to the rest of the virtual car. So, combining the basic dimensions I'd clubbed together from SusProg for my default upright, I set to work. The first, and most obvious problem was that I'd need to shift the lower mounting inboard by around 50mm so that it wouldn't foul on the brak disc. Susprog works on individual points and doesn't allow for such piffling considerations as the diameter of the rod ends that will actually be in use. Not a big issue, but I'll have to revisit the location of the upper mounting as well to keep the zero offset kingpin inclination I want. Still, it's only software and time rather than swearing in the garage 'cause you've mucked up another set of calculations.

So, next job was to make a mounting for the hub unit - nice and easy and there's a nice big hole in the middle for weight saving purposes. After giving it a nominal 25mm thickness, I did a quick and dirty check with CosmosWorks (the inbuilt FEA) package which reckoned on a safety margin of 8 with a 250kg load on the mounting bolts. I then added extensions for the lower mounting and the steering arm which gives the object shown above.

Final task of the day was to start building up a complete upright design so that I can be sure that I'm not doing anything silly with clearances. Yep, you've guessed it - I've manage to clash the steering arm with the brake calliper itself, and not by a small amount either:

So I have two choices:

1. Move the steering arm or calliper to the front to remove the clash - nice and easy, although I did flirt briefly with the idea of installing the calliper at the bottom of the wheel for c of g lowering purposes until I realise that I'd then be clashing with the lower mounting eye instead
2. Move the steering arm further inboard to avoid the clash - again easy to do in virtual space but a right bugger for anyone who actually wants to make the thing

I think 1 makes more sense and I'm more inclined to move the calliper than the steering arm because I want to leave the far front of the car free for a crushable structure and the radiator (if I can't get enough cooling using side ducts) rather than filling the space up with a steering rack.

Oh well, back to the coal face...

I love SolidWorks...

because it links in with 3dContentCentral. Anyone who does a lot of designing will tell you that if you haven't got decent backup from suppliers then you spend an inordinate amount of time reverse engineering standard components to be able to insert them into your virtual assemblies. Yesterday I was talking about designing my own hubs so as to be able to press on with the upright design. SKF have their complete bearing catalogue online within 3dContentCentral so it was a case of dragging components off-the-shelf and putting them into the design. So a quick 15 minutes (and I'm not kidding here) later, we have a nice working hub design that I can now use for reference. If all comes to the worst, I can simply get those manufactured and sold.
The hub isn't perfect yet - I haven't made the central spindle long enough to fully engage with an M20 nut; there's no dust cap for the bearings, although given the lack of usage and (hopefully) the attention to detail of most racers, it's probably not necessary; the tolerance issues haven't been ironed out (everything is a perfect sliding fit with 0.000000mm of clearance) and I'm not sure it'll be gold anodised if ever I manufacture it. Pimpy looking components do sell a car and I'm reliably informed by people with more taste (i.e. everyone) that purple is the new gold.

Still, it's something to be going on with...

More on uprights...

OK, I've started bolting things together virtually. By putting the calliper and brake disc together, I've worked out that in order for the brake disc to line up with the centre of the contact patch we'll need wheels with an offset of 42mm (luckily that's a nice common offset) and then everything will fit comfortably under the 13" rims.

The next task is to take the data from SusProg in terms of the location of the upright mounting. Luckily SusProg is sensibly designed so that the uprights aren't measured relative to the vehicle datum (i.e. measured from a virtual point at the intersection of the vehicle centreline and the front axle centreline) but relative to the mounting face on the upright. This saves a lot of unnecessary trigonometry, although I must make sure to subtract the width of the disc mounting face as this is effectively a spacer between the upright and the wheel.

The thing that is holding me back from finishing this first component is that I haven't had time to measure up a suitable hub yet. I'm still toying with the idea of doing my own, but for now I'll just mock up an estimated hub and go from there. The joy of CAD is that it's inordinately easy to change something right at the top of the model and let all the changes percolate through. I'm a really lazy person at heart if I can be...

The picture above is a very quick mock-up - I put the calliper and disk together with a basic plate so I could measure up how much space there was between the calliper mounting bolts and the back face of the mounting bell. With that number (it's 49.5 mm for anyone interested), I can get everything else together.

First CAD bits

I know they're not much to look at, but at least it's a start. The drawing above is straight out of the AP racing catalogue and is their 10" disc with integral mounting bell. I had wondered about designing my own hub-cum-mounting bell but as I've said earlier, I don't want to price the car out of the market and the less machining that potential racers have to do the better. For those who like looking at catalogues it's part number CP2222-258/59

Now, I know this looks unbelievably unlike a Wilwood Powerlite calliper, but don't worry. What I've done is create a volume model which encompasses the maximum dimensions for the calliper. If this fits under the virtual wheel, then I'll know I haven't got a problem when it comes to the real thing. The last thing I want to do is waste oodles of time generating a micron perfect facsimile of the calliper only to find that tolerance build-ups in the real thing lead to an expensive aluminium-to-aluminium contact.

Anyway, with these two bits designed I can move on to getting the upright designed. I'll be trying to make the upright as light as possible, by designing pockets into it. So that I don't make the thing ludicrously weak, I'll be taking advantage of the built-in FEA to SolidWorks.

Uprights...

I'm back... I did take the laptop away with me to a very nice part of Wales, but it was so nice, I didn't actually take it out of the bag at any point during the week. Anyway, as I've still got a week before I have to go back to work, I've got some time to crack on with the design.

For my other reader, the upright is the business end of each wheel station. It carries the hub that the wheel bolts onto; the outboard pickup points for the suspension; the joint for the steering arm; the brake calliper and the brake disc as well. In short it has to resist all the road loads into the chassis without deforming.

There are three ways of manufacturing an upright: casting, machining and fabrication. Now, while I do have a fully working forge, I'd wager that very few hobbyist builders out there do. Casting is wonderful for many reasons but for small runs it's extremely expensive and you tend to have to do a lot of machining on the finished casting anyway. So I can probably safely discount it.

Machining is what I'm best at, but the cost of a lump of billet might scare a few people - a 2" x 2" x 3000mm (don't you just love industries where Imperial and Metric dimensions get mixed about) billet costs around 150 GBP and with a decent design most of that billet will be converted into swarf. Most 'professional' race cars tend to use machined billet uprights (the McLaren F1 did as well) and as it's someone else's money when we're living in virtuality, I'm not necessarily worried about wastage.

Fabrication is a very efficient way of manufacture, but it requires real craftsmanship to get an accurate finished item with no structural weaknesses. A good quality fabricated upright probably isn't going to come out of an amateur's garage with the aid of a Machine Mart MIG welder. I don't think I'd be happy racing around with something I've welded together, and welding pretty much guarantees the use of steel and it's resultant weight penalty.

So, machining it is and the next job is to get a few parts modelled up for further use: the brake disc and the calliper space model (i.e. I only need the outside dimensions rather than an exact 3d model with all the fillets, chamfers and the like). I'll be back after I've got busy with Solidworks.

More on Braking

Because I like nothing more than fiddling, I've put the majority of my calculations (I've left out the bit about effective pad radius for the moment) into a nice Excel spreadsheet and included some stuff about specifying the brake bias bar and the master cylinder diameters for front and rear. I've uploaded it here for your general delectation and amusement. It's in Excel format, although the original was done in OpenOffice...

I'm disappearing off on holiday for a week or so, so my three readers will have to amuse themselves elsewhere...

13" or 14"?

My other commenter (my god, I'm starting to sound like Terry Wogan) wondered why I was going with 14" wheels, when 13" wheels would be lighter and the brakes that I could fit underneath would be more than man enough for the task - and if someone wanted to fit 14" rims, there would be nothing stopping them. The short answer is that I had no strong feelings on the subject, other than the fact that I like having plenty of space around the upright for kinematics reasons. I did however promise to do some calculations and get back to him. OK, here goes...

Minimum weight for the car is 560kg and I'm currently working with a wheelbase of 2.2 metre. We're going to be mid-engined, so I wouldn't be too surprised is we have a weight distribution somewhat towards the rear, say around 45% Front : 55% Rear. Centre of gravity height is unknown. The only useful figures I've got (I've only ever done testing of military vehicles, which probably doesn't help much) are for a Toyota MR2 at 0.485m above ground. We'll be a smidgin lower and the absence of a roof on the car will take that lower still, so I'd estimate (in finest sticking a finger in the air fashion) a centre of gravity around the 0.42m mark.

The tyres for the formula (Yokohama A048R) can produce a static coefficient of friction of around 1.2-1.3, but we may well have plenty of downforce, so it's not entirely inconceivable that we could be producing around 1.5g under braking. So, a quick spurt of calculation gives the following weight distribution:

	Front	Rear
Nearside	123.75 kg	151.25 kg
Offside	123.75 kg	151.25 kg

Let's now look at the weight distribution under braking. When you brake, weight is taken off the rear wheels and put on the front wheels. The amount of weight transferred is a function of mass, rate of deceleration, wheelbase and centre of gravity height. The governing equation is:

Weight Transfer = Mass x Deceleration x Centre of Gravity Height / Wheelbase

So with 1.5g deceleration, we get just under 1.6 kN of weight transferred (or 160.3 kg of mass). That's a fair chunk of mass - we end up with just 71.1 kg of mass on each rear wheel when braking, which wouldn't give me huge confidence under braking unless there was a nice, healthy chunk of downforce to screw the rear wheels down. We also have 203.9 kg on each front wheel.

At 1.5g of braking, and assuming we've wound the bias adjusters to the perfect position, each front wheel has to provide 203.9x9.81x1.5 = 3 kN of deceleration force. George Polley's website suggests that the overall diameter of a 13" A048R tyre is 550 mm, which gives us a torque produced by the braking system of 3x0.55/2 = 0.825 kNm.

I've been looking at two different brake callipers - both can use a 276mm diameter disc (that's 10.5" in old money give or take a gnat's chuff). The bigger, 4-piston, calliper uses a 46.1mm high brake pad and 4 1.25" diameter pistons and the smaller, 2-piston, calliper uses a 38.4mm high brake pad and two 1 5/8" diameter pistons. The coefficient of a brake pad varies a bit, but Ferodo DS2500 compound (I know a lot of racers use Mintex, but Mintex don't publish their mu values and Ferodo do) has a mu value of 0.5, so effectively the deceleration force at the rotor needs to be doubled to give a force at the piston.

I'm going to assume an even distribution of force across the whole of the brake pad so that the centroid of that force is in its centre. So the effective radius for the application of the braking force is going to be (disc diameter - pad height) / 2, or 110.45mm for the 4-piston callipers and 114.3mm for the 2-piston callipers. Torque = Force x Distance, so the piston force = torque / distance (x 2 to allow for the pad friction coefficient). Running with the values earlier, we get the following numbers: 7.2 kN for the 2-piston callipers and 7.5 kN for the 4 piston callipers.

Pressure = Force / Area, so we can now calculate the pressure required in the braking lines at the front. It comes out at 24 Bar for the 4 piston design and 27 Bar for the 2 piston design. The callipers are rated at 30 Bar, so they're man enough for the job and all we need to do now is sort out whether our poor race will actually be able to apply enough pressure at the brakes to get that level of deceleration. The ECE braking regulations mandate a brake pedal force of around 500N for stopping with the engine disengaged. So if we assume this is our pedal force and a pedal ratio (amplification by the lever action) of around 5, we have a pedal force of 2.5 kN. This means we need an area ratio of around 3, i.e. the area of the calliper pistons needs to be no more than three times the area of the master cylinder piston. For our 4 piston calliper we get a piston diameter of 36mm and for our 2 piston callipers we get a maximum diameter of 58 mm. These comfortably fit within the bounds of what is available and give plenty of options for fine tuning by having a smaller pedal force ratio.

So, in summary, the 2 piston callipers and 13" wheels will be fine, and in a desire to make as many people happy as possible, I'll engineer the uprights and suspension to fit under 13" rims. I've got a nice steel rim handy - I'll measure that if this rain ever stops falling.

My first radical rethink...

actually it's probably my second or third. This one stems from a close study of both Milliken and Milliken and Katz while in my favourite room of requirement. M&M reports a lot of results from the F1 ground effect era which indicates that the best downforce was actually developed with a ground clearance of 75mm (which just happens to be the minimum ground clearance for RGB) and there are some useful wind tunnel results from vehicles with underbody tunnels and no sealing sideskirts. So with careful consideration paid to the shape of the underside of the chassis, it looks like there might be the possibility of generating useful downforce for the car. Hmm.... I had been slightly upbraided by my solitary commenter (thanks Steve) for having a pushrod suspension system in the first picture produced out of SusProg. If I do manage to get significant downforce out of the car then having a pushrod system will make it easier to engineer in a third spring to deal with the extra aero-loading. I quite liked the idea of a pushrod suspension in any case as it makes it far easier to adjust the suspension in terms of ride height and damper adjustment as you can get at the adjusters simply by taking the bodywork off rather than having to get down on your hands and knees and contort your wrist around the suspension arms, driveshafts and brakes. I have to do that now with my daily driver and it's not a whole heap of fun.

I've also been thinking about the uprights as well, or more specifically the hubs that are going to bolt into them. I'm not a big fan of reinventing the wheel, and HiSpec Motorsports do very nice CNC machined (and you can't beat CNC bling) hubs based on patterns of classic Ford boxes of the 1970s and it would be churlish not to use something easily accessible just to be different. I know of at least one racer using these, so I might sidle up to him at some point in the future and ask to come round with my vernier callipers and see if I can come and measure them for dimensions. Once I have those dimensions, I can work on sorting out the other positions on the upright. The other thing I need to work out is how to avoid the dreaded REIB problem. I could make the suspension completely non-adjustable, but I reckon there are two main problems - firstly, I can't imagine anyone constructing the car is going to be so accurate that the designed geometry is actually going to be the real-life geometry and a bit of fiddling is bound to be necessary; and secondly, giving someone a non-adjustable racecar is bound to be a recipe for disaster. A lot of the RGB racers seems to be inveterate fiddlers.

Of course, I could just ignore the fact that I'm using rod ends in bending and make them nice and stout instead. As I'm not planning on winning a Formula SAE design competition and everyone else seems to manage fine with that sort of structure. I could get away with it, but every engineering bone in my system is yelling at me not to accept such compromises and spend 6 months developing a beautiful adjustment system. Knowing my luck such a system would weigh more than the rest of the car put together, although I do like the eccentric bolt system that's on my Mazda and it would limit the amount of adjustment options to what is sane.

Anyway, time to get back to the AP Racing catalogue and find a suitable set of callipers and discs for the virtual racer. Once I have both, and the dimensions of the hub, I can sort out a wheel offset and then, finally, the position of the suspension joints. Why do I need all this information? I want centre point steering on the car. This means that the line passing through the wishbone mounting points on the upright passes through the centre of the contact patch and there is no kickback through the steering when longitudinal forces are applied to the suspension. Kickback drops driver confidence and as I've stated before, an under-confident driver is a slow driver.

In the last post, I'd sort of produced a ballpark figure for the space inside the wheel rim of around 310mm. I know that the rim slopes inward at the front and I'd probably have more to play with than that provided the brake disk and calliper wasn't too deeply embedded. So, a quick search through the AP catalogue turned up the fact that 254mm discs aren't supported by 4-piston callipers, but 267mm discs are. Of course when you look at the outside radius of the callipers they need 312mm of space inside the rim. Close but scarily close to being a show stopper. There's plenty of options in the 2-piston calliper range and frankly this car is going to weigh very little. But I just have this horrible sneaking suspicion that if we do get sufficient downforce then 2-pot callipers may not be man enough for the task. I'm thinking here of braking down at the end of the Revett straight at Snetterton - it's not somewhere I'd like to run out of brakes. I'll wait until I can measure a 14" alloy (actually, come to think of it, there's five sitting in the garage ready for the kit car it looks like I'll never finish building because I'm better on a CAD system than I am with my hands.) before making a firm decision. Having seen the trouble others have had getting brakes and uprights to talk nicely to each other, I don't want to get this fundamental wrong.

Uprights and wheels

I've been doing a little playing around with SusProg in order to look at the fundamental effects of locating the instant centre along the vehicle centreline. I've revised my estimate of track after looking at the track values of someone else's car - I'm now looking at a track width of around 650mm. Anyway, I've modelled two suspensions - one with a fairly conventional wishbone setup and one with sharply inclined wishbones so that the instant centre is along the centreline.

Look at the two photos:


The upper one is the conventional. The pictures aren't to scale (blame finger trouble on my part), although the grids are identical at 40mm spacing. The big black dot is the ground on the centreline and we're looking at 40mm of bump travel here. The obvious difference is that there is a lot of camber change in the 'centreline' suspension - this is to be expected, as using such suspension gives a very fixed virtual swing arm length (approximately half the track width), while the normal suspension has a significantly longer swing arm and less camber change in bump. The question is whether the absence of camber change in roll makes up for the change in bump. The short answer is probably, but only at the rear. At the front the camber change that would result in the wheel acting like a gyroscope and kicking back through the steering. That would be something that could decrease driver confidence and is therefore a bad thing as far as my design principles go.

I'll keep tweaking the values for a while and see if I can get to a better centre point solution. I'm pretty limited in where I can put the bottom wishbone joint as it can't be lower than the 75mm limit mandated in the rules. As I'm planning to design my own uprights, I've got a fair bit of flexibility in where I put the roll centre so I can lower it from where it currently is to prevent jacking of the vehicle under cornering.

I'm getting to the stage where I should really stop fiddling with SusProg and work out what shape the uprights are. Key to this is going to be being able to fit a suitable set of brakes within the wheel envelope. This might sound easy, but I know at least one racer who had all sorts of problems trying to get a set of brakes to fit. So first job is to find a suitable wheel and get some measurements off it. I'm limited to 6" wide wheels and luckily, I've got a dented 16" alloy wheel sitting in the shed (before any of you comment, I know that the A048R spec tyres don't come in 16" sizes, but I wanted a quick and dirty check on what I had here before I pester one of you for a measuring sessions). A quick bit of steel tapery and I get a 360mm envelope within which to work. If I assume that there's no change in wheel web thickness, each 1" reduction in rim size means 25mm less envelop to play with and I doubt there's many 6"x15" wheels out there, so I should think that a 14" wheel rim is likely to be the norm. Certainly the above-mentioned racer is running 14" wheels. So, I think the maximum envelop I have to work with is going to be 310mm. Now all I need is some brake callipers to fit underneath.

One quick glance at the Wilwood catalogue and their Powerlite callipers will do the trick. The trouble is that in order to pass scrutineering the car needs a working handbrake and the 'add-on' callipers I've seen probably won't fit comfortably inside the wheel. So, the obvious choice is HiSpec Motorsport, who do specific callipers with a mechanical handbrake that doesn't impinge on the outside of the calliper. Their version of the Powerlite looks very similar, although their mounting diagrams leave a little to be desired. I'll assume a 254mm disc for now.

Kinematics and Roll Centres

At its basest level, the role of the suspension is to hang the wheel off the chassis and stop it flailing around. Any object can have six ways of moving - three displacements (up and down, inwards and outwards and forwards and backwards) and three rotations. The suspension is meant to restrict five of those movements relative to the chassis so that, in theory, the only movement is up and down. If you have ball joints at each end of the suspension links, you need five separate links to control five out of the six possible ways of moving - hence the term multi-link suspension.

I've already decided to use double wishbone suspension for the car and each of those arms is equivalent to 2 separate links. This means we need an extra link - the toe link, joining the upright to the chassis, otherwise the upright will be free to rotate about an axis running between the top and bottom ball joints on the upright. On the rear this link can be fixed, but on the front it is joined to the ends of the steering rack so that the racer can actually negotiate corners. I'm actually considering having identical suspension front and rear so that it cuts down on the component rate, i.e. four identical uprights with either a fixed toe link or a steering arm rather than having four separate uprights per car. As anyone who has worked in a manufacturing environment will tell you it's far easier and cheaper to build four the same than four different.

Anyway, I digress... Analysis of five separate links is not a trivial matter but a bit of careful inspection of a suspension will show that for a given position of wheel and chassis, you can replace the entire suspension with a single arm and its kinematic and force behaviour will be the same. The point where this single arm pivots is called the instant centre of the suspension. The further away from the wheel this instant centre is, the less change there is in camber as the wheel moves in bump and rebound. The classic case is a solid axle suspension where the instant centre is effectively positioned off at infinity so that there is no camber change as the suspension rolls. A similar case is where the wishbones are parallel. Movement in bump causes no change in camber, but roll causes significant camber change.

Once you know the location of the instant centre, you can calculate the position of the roll centre. This is defined as a point where a lateral force can be applied to the car which would cause no roll of the body. Effectively it's a line of action where the side force from the tyres is transmitted into the body. If the line of action happens to pass through the centre of gravity, there is no roll and if the line of action is above the centre of gravity then the car will lean into the curve. Most of the time, the roll centre is below the centre of gravity and the car leans outwards when you steer. The roll centre is found by joining a line from the centre of the contact patch to the instant centre. Where these two lines (one for each side of the car) intersect is the kinematic roll centre.

Roll centres are important as they control how much weight is transferred to which wheel when you corner. The side force generated by a tyre is a function of three things: the weight supported by the tyre, the camber angle of the tyre and the slip angle - the angle between the direction of travel of the tyre and its heading. Controlling how much weight is on each tyre is a way of controlling its handling and it's something we'll come back to later when we get to sorting out the spring and damper rates.

We can't control the total amount of weight transferred - that's a function of how much 'g' we're pulling in a corner, the height of the centre of gravity and the track of the car. F1 engineers have been trying to put the c of g below ground level for many years with little success, and I'm sure I'm going to have similar success on that front. Having a roll centre close to the c of g is achievable and will limit the amount of roll of the car, making it more predictable. The only problem we have to consider is jacking. Anyone of a certain age might remember the joy of driving a VW Beetle close to the limit. The Beetle has swing arm suspension at the rear - instead of wishbones it used the half shaft to support the wheel. When you cornered the force was transmitted up the half shaft and with a lot of roll this would jack the rear of the car upwards and you could get the rear wheel to tuck under the car and lead to a Beetle-shaped hole in the nearest hedge.

Anyway, enough waffle, back to design. In the last post I stated that I wanted no camber change in roll and minimal migration of the roll centre. The only way to achieve this is by having the instant centres of both sides of the suspension meeting each other on the centreline of the car. This will result in shorter equivalent swing arms (i.e. the length of the imaginary bar joining the centre of the upright to the instant centre) than could otherwise be achieved. In other words, using this method there will be more camber change in bump using this system than there perhaps could be. The only way to get a reduction in camber change is to have as wide a track as possible. Until I can get out and measure someone's bodywork (no part of the tyre is allowed outside the envelop of the bodywork under the rules, which sort of rules out a Formula Ford as a design concept), I don't know how large a track I can get away with. So for now, while I work with the concept, I'll make a few assumptions and assume the maximum width will be around 1400 mm.

BTW the picture above (click it to enlarge) is of a quick and dirty concept, which has a reasonably long equivalent swing arm length (where the three thin red and green lines converge is the instant centre), but around 40mm of lateral roll centre migration (the diagram is for when the car has rolled through two degrees). It's an OK concept, except the top wishbones are too close together to match with a sane set of rollbar backstays - in an attempt to keep a handle on weight, I'm trying to use as little spaceframe as possible, so integrating the suspension pickups with the roll bar seems a fairly good idea. I'll be back once I've done some tweaking to get the instant centres aligned.

I've got a copy of SusProg...

and I'm not afraid to use it. Reading through the regulations of the RGB championship, there's no ability to tune the engine from when it got separated from the motorcycle. So if you're going to build a successful racer, aside from a large amount of driving talent, you need to find other ways of gaining a competitive advantage over your fellow competitors. 'Proper' aerodynamics aren't allowed (and although there doesn't appear to be a limit on underbody aerodynamics, the minimum ride height of 75mm seems to not be of much help in generating some venturi-assisted downforce), there are minimum weights (although getting close to them seems to be a challenge for those who do indeed take the RGB regulations at their word rather than constructing a specialist lightweight chassis) and everyone is running the same tyres.

So it appears the only way to beat your fellow racers is to out-drive them, or for those with less talent, out-handle them. Here is where SusProg comes in. If you're incredibly rich, you can spend the GDP of a small African protectorate on kinematic simulation software like MSC Adams to help with your suspension design so that you don't have to rely on Colin Chapman's ethos of 'the suspension works great if you don't let it' to avoid all sorts of nasty kinematic and alignment problems.

As a former ride and handling engineer (OK, so most of the vehicles I helped engineer were green, extremely heavy and capable of dealing death over large distances), I'm afraid I treat the rest of a car as a black box - if it doesn't work, you get rid and find something else that does. I'm going to design the car from the wheels inward - create a suspension design that works, then stick a chassis on it. Using SusProg is key to this. It lets you design the suspension virtually and see how it works before you commit yourself to cutting your first bit of tubing.

I've already made a conscious decision to avoid using someone else's uprights to hang the wheels off. For a start, I haven't got the time or inclination to find some suitable uprights, sort out suitable brake discs, callipers and wheels so that they all work together and, more importantly, fit and then design a suspension that fits in with the limitations of the upright. I plan to design easily (at least easily if you've got access to a nice CNC milling machine) build-able (possibly even fabricate-able) uprights and then hang everything else from there.

Enough with the planning, lets get on with the design. I'll start at the back, not least because I only have to deal with the wheel moving up and down and not with having to steer as well. Using a double wishbone design is the obvious choice (everyone else designing racing cars seems to do the same thing) but then it all gets a bit more complex. We need to control what happens to the wheel when it rises up and down relative to the body. The two things we need to control are camber (the inclination of the wheel relative to the vertical) and toe (the rotation of the wheel about the vertical).

Let's start with toe. If your wheel steers itself as it goes over bumps this may not be a good thing. If there is enough self-steer the car will potentially be less stable. A less stable car leads to a less confident driver and a less confident driver is a slower driver. Sometimes this steering over bumps can be a good thing - Lotus use it on the Elise to improve stability with the steering that results counteracting the grip changes due to the change in loading on the contact patch. If you can find a copy of IMechE paper C466/014/93 (it's in the proceedings of the Vehicle Ride and Handling conference - take a look at C466/010/93 as well if you get the time as it's a report on what I was doing at the same time) it's all 'explained'. Personally, I think eliminating toe change altogether is an easier objective and hopefully a racer will prefer an absence of any taint to the feedback he gets from the car.

Camber is a bit more subtle. If you tilt a wheel over, instead of a nice oval contact patch between the tyre and the road, you get one shaped a bit like a banana. As the rubber rolls through the contact patch it is forced in a curved path rather than a straight one and this deviation provides a small sideways force. This is handy if the force acts in the direction you want to turn and less handy if it doesn't. As the suspension moves, it moves through some form of arc and this changes the inclination of the wheel and can lead to reductions or increases in the grip of the tyre. The arc is subtly different between the wheel moving in bump (where the chassis stays flat to the ground) and in roll (when the chassis tilts moving the suspension mounting positions relative to the ground)

Another thing to consider is traction. Potentially we are going to feed 180 bhp to the rear wheels and we want as large a contact patch as possible to avoid the wheels spinning and wasting acceleration potential. A cambered tyre has a smaller contact patch than one running upright on the road. The first racer on the gas in a corner carries the most speed out and has the lower lap time, so being able to put the power down with the car rolled over is a key issue to resolve.

So taking all this stream of consciousness out, I've come up with the following design parameters:

• Minimal camber change in roll (I'm hoping for zero change if possible, like the Porsche Carrera GT)
• A non-migrating roll centre (I'll talk about roll centres in a later post, but they're very important to vehicle handling)
• Low camber change in bump, and a negative camber change if possible
• Zero change in toe with bump

OK, so we've got some parameters to work with, let's start messing with SusProg...

Introduction

I'm bored and frustrated. I teach engineering in the British 'Further Education' sector, i.e. I'm allegedly not smart enough to teach undergraduates and anybody with a modicum of intelligence gets grabbed by the local schools to be taken on the path to university, leaving us with a curious mix of students who don't quite understand the point of education. Teaching does have it's side bonuses. I have a fully equipped workshop with some very expensive CNC machines in it and a CAD suite with Solidworks. Inspired by the wonderful DP1, I'm going to do something similar, only in a British style.

I have a few friends who race in the RGB series, run by the 750 Motor Club. The class seems to be a mix of classic (i.e. bolted together out of bits of 1970's vintage tat) kit cars, all using Japanese motorcycle engines. The cars have to be able to pass an MoT, although there is no requirement to actually have one. This does give a designer a great degree of freedom to work within the regulations, so I have a very basic plan:

• mid-engined racer with rear-wheel drive
• spaceframe chassis
• front or side mounted radiator(s)
• someone else's bodywork - the one thing I don't have the facilities to make is bodywork, so I'm thinking of begging/borrowing someone else's to drape over the chassis
• my design of suspension - before being dragged kicking and screaming into the halls of 'academia', I worked as a ride and handling engineer, so I should be able to make a decent fist of it...
  
• decently engineered front and side impact protection that hangs off the chassis, so that when if the driver makes a small error he shouldn't have to replace the chassis or get busy with a MiG welder in the paddock
  

From these humble idea, over the next few months, I plan to have a fully existing CAD model of a racer that I plan to leave on the Internet for posterity so that any stupid enlightened racer can put it together in a garage and have fun with. I'm not planning to do any manufacture myself, it's more therapy to stop me taking the students around the back of the workshop and committing physical violence with a 25.4mm diameter bar of tool steel.