My Sim: Angular Velocity

I said it would be in another post, so here it is! Not modelling differentials. I'm calculating the angular velocity of the wheels thus: FZ = weight on that wheel (uses weight transfer) Driven Wheels: angularAcc = { (totalTorque) / radius} / (FZ/GRAVITY) where totalTorque = (-resistanceForce * radius) + (engineTorque * gearboxReduction * radius) + (-brakeForce * radius) angularVel += angularAcc * deltaTime Undriven Wheels: I am assuming they are rolling at the same speed of the car angularAcc = carAcc angularVel += angularAcc * deltaTime However I am not sure how correct this is as there is no reference to how to calculate angular velocity. And effects like applying brakes should lock just the driven wheel in this case (as an undriven wheel doesnt account for brake forces in the above description, it is just the speed of the car) , and it does. However, if I release the brake, the wheel should roll again, but does not take into account the speed of the car, so it does not roll along, it stays locked. There is obviously error in the calculation, and I must be missing out some things. Using the relaxation length approach to calculating slip ratio, the car starts and stops, I am assuming (and hoping) that it is due to a problem with this calculation. Please help! Thanks! I know I can rely on you guys!

Hi Alex, right, onto the questions then :) On Wed, 10 Apr 2002, Alex Smith wrote:

Quoted text (12 lines)

> I said it would be in another post, so here it is! > Not modelling differentials. I'm calculating the angular velocity of the > wheels thus: > > FZ = weight on that wheel (uses weight transfer) > > Driven Wheels: > angularAcc = { (totalTorque) / radius} / (FZ/GRAVITY) > where totalTorque = (-resistanceForce * radius) + (engineTorque * > gearboxReduction * radius) + (-brakeForce * radius) > > angularVel += angularAcc * deltaTime

This is not as relevant, but there's a slight error in the first equation. The value you should divide by is the effective moment of inertia on that wheel, not FZ/GRAVITY. That moment is quite difficult to calculate since it is a joint contribution from all the parts linking to the wheel (not to mention that the diff makes matters even more complex), but let's for now assume that only wheels contribute as we want the stuff to get rolling first, right :)? A typical total moment of inertia MOI for a wheel is of the order of magnitude 1 kg m m, so that might be the value you should use for now. The rest seems quite alright, though, although one would typically define not a brakeforce but a braketorque, but that's just a matter of definitions. > > Undriven Wheels: I am assuming they are rolling at the same speed of the > car > angularAcc = carAcc > angularVel += angularAcc * deltaTime > Do not assume too much. Treat them exactly as the driven ones, but do not put any engine torque to them. It is true that for the most part this approximation is quite correct, but I believe this might be the problem for your calculations. What you will also notice is that it's hard to define the braking force for when the wheel is locked, much like in the case of a tyre force at rest. But for now, let the braking force (torque) just point the opposite to the angular velocity, as all this will induce will be a slight oscillation of locked wheels (hopefully :) ). I believe this will for the most part help with the problems described bellow. Caution: you might need to increase the frequency of physics updates once you plug the moments of inertia in, as this tends to make the wheels adapt very quickly.

Quoted text (17 lines)

> However I am not sure how correct this is as there is no reference to how to > calculate angular velocity. And effects like applying brakes should lock > just the driven wheel in this case > (as an undriven wheel doesnt account for brake forces in the above > description, it is just the speed of the car) > , and it does. However, if I release the brake, the wheel should roll again, > but does not take into > account the speed of the car, so it does not roll along, it stays locked. > > There is obviously error in the calculation, and I must be missing out some > things. > Using the relaxation length approach to calculating slip ratio, the car > starts and stops, I am assuming (and > hoping) that it is due to a problem with this calculation. > > Please help! Thanks! I know I can rely on you guys! >

You can rely on us, but only if you really trust us (I wouldn't be so certain myself ;) ). -Gregor

Gregor Veble <[email hidden]> wrote in message news:[email hidden]... > A typical total moment of inertia MOI for > a wheel is of the order of magnitude 1 kg m m, so that might be the value > you should use for now. The rest seems quite alright, though, hmm, not quite sure I understand the units. > Do not assume too much. Treat them exactly as the driven ones, but do not > put any engine torque to them. It is true that for the most part this > approximation is quite correct, but I believe this might be the problem > for your calculations. In my implementation (which is wrong :), the undriven wheels have no forward torque as they are not driven by the engine which is why the only way I can make them rotate is by setting the angularVelocity directly, not calculating it by its torque. Am I giving the wheel a torque due to the car accelerating? In that case would I need a special case in the wheel.getTorque() function like if (wheel is not driven) torque = carAcceleration * wheel.load/GRAVITY * radius [or inertia :)] ?? > What you will also notice is that it's hard to define the braking force > for when the wheel is locked, much like in the case of a tyre force at > rest. But for now, let the braking force (torque) just point the opposite > to the angular velocity, as all this will induce will be a slight > oscillation of locked wheels (hopefully :) ). I believe this will for the > most part help with the problems described bellow. I can get the wheels to lock, but when I want them to start rolling again by releasing the brake, it doesn't because there is no torque related to how fast the road is moving beneath it. However if I add this torque to the driving torque, the car would shoot off (?) aaaAAAArgh! Maybe I should just start my wheel model from scratch again :(

Get the torque from the ground...keep deriving the slip ratio.. the wheel will be slower than the ground and will generate a Fx... but then u have to feedback that Fx into the wheel again.. opposite direction... and it'll become a positive torque..and there it is your wheel accellerating to keep up with the ground... I hope this'll help. Stefano Casillo "Alex Smith" <[email hidden]> wrote in message news:a91tr5$o76$[email hidden]... > > Gregor Veble <[email hidden]> wrote in message > news:[email hidden]... > > > A typical total moment of inertia MOI for > > a wheel is of the order of magnitude 1 kg m m, so that might be thevalue > > you should use for now. The rest seems quite alright, though, > > hmm, not quite sure I understand the units. > > > Do not assume too much. Treat them exactly as the driven ones, but donot > > put any engine torque to them. It is true that for the most part this > > approximation is quite correct, but I believe this might be the problem > > for your calculations. > > In my implementation (which is wrong :), the undriven wheels have noforward > torque > as they are not driven by the engine which is why the only way I can make > them > rotate is by setting the angularVelocity directly, not calculating it byits

Quoted text (14 lines)

> torque. > Am I giving the wheel a torque due to the car accelerating? > > In that case would I need a special case in the wheel.getTorque() function > like > > if (wheel is not driven) > torque = carAcceleration * wheel.load/GRAVITY * radius [or > inertia :)] > > ?? > > What you will also notice is that it's hard to define the braking force > > for when the wheel is locked, much like in the case of a tyre force at > > rest. But for now, let the braking force (torque) just point the

opposite > > to the angular velocity, as all this will induce will be a slight > > oscillation of locked wheels (hopefully :) ). I believe this will forthe > > most part help with the problems described bellow. > > I can get the wheels to lock, but when I want them to start rolling again > by releasing the brake, it doesn't because there is no torque related tohow

Quoted text (8 lines)

> fast > the road is moving beneath it. However if I add this torque to the driving > torque, > the car would shoot off (?) > > aaaAAAArgh! Maybe I should just start my wheel model from scratch again :( > >

Stefano Casillo <[email hidden]> wrote in message news:a92fo1$cc6$[email hidden]... > Get the torque from the ground...keep deriving the slip ratio.. the wheel > will be slower than the ground and will generate a Fx... but then u haveto

Quoted text (7 lines)

> feedback that Fx into the wheel again.. opposite direction... and it'll > become a positive torque..and there it is your wheel accellerating to keep > up with the ground... > > I hope this'll help. > > Stefano Casillo

So roadTorque = -wheel.FX * radius ?? (unsure) then angularAcc = (wheelTorque + roadTorque ) / inertia this does indeed produce the desired effect!! However, the increase in speed of the driven wheels is very uneven, and this must be due to the changing road torque, which is dependant on the slip ratio. Also, it limits the top speed and in high gears it cannot reach the redline. Any suggestions!?

If u use that for the driven wheels the you have to calculate the inertia for all the block wheels, diff, gear, engine connected.. I wouldnt know really... in my sim works just nice... also not so much low speed instability.. but you have to be tricky with the brakes code. keep expermimenting... I think that's the way to go... "Alex Smith" <[email hidden]> wrote in message news:a92jc0$jgr$[email hidden]... > > > > Stefano Casillo <[email hidden]> wrote in message > news:a92fo1$cc6$[email hidden]... > > Get the torque from the ground...keep deriving the slip ratio.. thewheel > > will be slower than the ground and will generate a Fx... but then u have > to > > feedback that Fx into the wheel again.. opposite direction... and it'll > > become a positive torque..and there it is your wheel accellerating tokeep

Quoted text (14 lines)

> > up with the ground... > > > > I hope this'll help. > > > > Stefano Casillo > > So > roadTorque = -wheel.FX * radius ?? (unsure) > > then > angularAcc = (wheelTorque + roadTorque ) / inertia > > this does indeed produce the desired effect!! > However, the increase in speed of the driven wheels is very uneven, and

this > must be due > to the changing road torque, which is dependant on the slip ratio. Also,it > limits the > top speed and in high gears it cannot reach the redline. > > Any suggestions!? > >

"Alex Smith" <[email hidden]> wrote in message news:a91e1t$1aa$[email hidden]...

Quoted text (19 lines)

> I said it would be in another post, so here it is! > Not modelling differentials. I'm calculating the angular velocity of the > wheels thus: > > FZ = weight on that wheel (uses weight transfer) > > Driven Wheels: > angularAcc = { (totalTorque) / radius} / (FZ/GRAVITY) > where totalTorque = (-resistanceForce * radius) + (engineTorque * > gearboxReduction * radius) + (-brakeForce * radius) > > angularVel += angularAcc * deltaTime > > Undriven Wheels: I am assuming they are rolling at the same speed of the > car > angularAcc = carAcc > angularVel += angularAcc * deltaTime > > However I am not sure how correct this is as there is no reference to how

to > calculate angular velocity. And effects like applying brakes should lock > just the driven wheel in this case > (as an undriven wheel doesnt account for brake forces in the above > description, it is just the speed of the car) > , and it does. However, if I release the brake, the wheel should rollagain, > but does not take into > account the speed of the car, so it does not roll along, it stays locked. > > There is obviously error in the calculation, and I must be missing outsome

Quoted text (8 lines)

> things. > Using the relaxation length approach to calculating slip ratio, the car > starts and stops, I am assuming (and > hoping) that it is due to a problem with this calculation. > > Please help! Thanks! I know I can rely on you guys! > >

Hi Alex! I'm not sure whether others have answered this or not yet (blame the awful news server/reader), so here it goes (again :) )... On Wed, 10 Apr 2002, Alex Smith wrote:

Quoted text (10 lines)

> > Gregor Veble <[email hidden]> wrote in message > news:[email hidden]... > > > A typical total moment of inertia MOI for > > a wheel is of the order of magnitude 1 kg m m, so that might be the value > > you should use for now. The rest seems quite alright, though, > > hmm, not quite sure I understand the units. >

Let's do a review; angular acceleration has units of rad/(s*s). Radians aren't really units (as they measure arclength divided by radius, which is then unitless), so what you have is just 1/(s*s). Ang_accel=M/J, where M is torque and since it is given as force times distance, the units are N * m=kg*m/(s*s) * m. To get the proper units for J which is the moment of inertia it is clear that only kg*m*m will do.

Quoted text (13 lines)

> > Do not assume too much. Treat them exactly as the driven ones, but do not > > put any engine torque to them. It is true that for the most part this > > approximation is quite correct, but I believe this might be the problem > > for your calculations. > > In my implementation (which is wrong :), the undriven wheels have no forward > torque > as they are not driven by the engine which is why the only way I can make > them > rotate is by setting the angularVelocity directly, not calculating it by its > torque. > Am I giving the wheel a torque due to the car accelerating? >

The undriven wheels in a stationary situation indeed match the road speed and as such have no forward torque indeed. However, imagine now that the wheel speed (ang vel* R) doesn't exactly match the road speed. What happens is that a slip angle becomes nonzero, and this in turn creates a (maybe very small) longitudinal force on the wheel which makes the wheel turn a bit faster until after a while it matches road speed again. The moral is that you should not set the road speed equal to wheel speed by force, as this should follow naturally from the calculations of slip ratios on the front wheel, the resulting longitudinal forces and the updated rotational dynamics of those wheels

Quoted text (7 lines)

> In that case would I need a special case in the wheel.getTorque() function > like > > if (wheel is not driven) > torque = carAcceleration * wheel.load/GRAVITY * radius [or > inertia :)] >

Do not use a different method for the front and back wheels. As explained above, the udriven wheels should have exactly the same equations as the driven ones (forgetting diffs now), except that on the undriven ones there is no driving torque. Just use the same code for the undriven ones as you do for the driven ones, set the driving torque to 0 and off you go, you'll see that (should all else be ok :) ) it'll work just as it should.

Quoted text (13 lines)

> > What you will also notice is that it's hard to define the braking force > > for when the wheel is locked, much like in the case of a tyre force at > > rest. But for now, let the braking force (torque) just point the opposite > > to the angular velocity, as all this will induce will be a slight > > oscillation of locked wheels (hopefully :) ). I believe this will for the > > most part help with the problems described bellow. > > I can get the wheels to lock, but when I want them to start rolling again > by releasing the brake, it doesn't because there is no torque related to how > fast > the road is moving beneath it. However if I add this torque to the driving > torque, > the car would shoot off (?)

As told before, if you do the undriven wheels the same way as the driven ones, when you lock the undriven ones you will develop a -1 slip ratio which, after the wheel gets unlocked, will be responsible for getting the wheel back to the road speed without any other input. Just plug it all in and see physics do its magic. :) -Gregor

On Wed, 10 Apr 2002 13:17:49 +0000 (UTC), "Alex Smith" <[email hidden]> wrote:

Quoted text (16 lines)

>Not modelling differentials. I'm calculating the angular velocity of the >wheels thus: > >FZ = weight on that wheel (uses weight transfer) > >Driven Wheels: >angularAcc = { (totalTorque) / radius} / (FZ/GRAVITY) >where totalTorque = (-resistanceForce * radius) + (engineTorque * >gearboxReduction * radius) + (-brakeForce * radius) > >angularVel += angularAcc * deltaTime > >Undriven Wheels: I am assuming they are rolling at the same speed of the >car >angularAcc = carAcc >angularVel += angularAcc * deltaTime

The car acceleration is different from the wheel angular acc, because one is linear, and the other one is round (depending on radius of the wheel at least). So if you simplify by saying the undriven wheels have the speed to match that of the car, you could more simply do a direct: angularVel=carVel/(2*PI*wheelRadius) or some factor to that effect. ;-) (math from the top of my head isn't my strong point) In fact, you should calculate slipRatio on the undriven wheels themselves, then apply the resulting Fx force as torque (using T=F*r), and then use that torque in: angularAcc=torque/wheelSpinInertia. It will follow the car velocity by itself that way. Ruud van Gaal Free car sim: http://www.racer.nl/ Pencil art : http://www.marketgraph.nl/gallery/