Car physics; rear/front differential ratio and velocity

Hi all, As I was/am adding a 4WD driveline, I was wondering about deriving velocity (for the dashboard velocity dial) from the gearbox. Suppose you have 3 differentials, a viscous one (center) and 2 other types in front and rear. If the front diff ratio is different from the rear diff ratio (where ratio is the inherent gearing ratio from ring gear to side axles), or if the front and rear wheels have different radii, how would you derive 'velocity' for your dial? For a single diff, I can solve the relationship between gearbox speed (=driveshaft speed) and wheels by the formula: perceivedVelocity=gearbox->rotVel*diffRatio*wheelRadius (as rotVel is in radians/sec, the circumference of the wheel, 2*PI*wheelRadius, falls out and you're left with just the above). The problem seems that for more than 1 diff, if the front and rear have a different 'diffRatio*wheelRadius' product, then depending on where the torque flows most, you get a different (inaccurate) velocity dial. Does anybody know how this is solved in real cars? I would perhaps guess that the differential ratios in both front and rear diffs are the same, but that still doesn't account for differences in wheel radii. BTW; A small other question for some clutch analysis. It seems my street car (Peugeot 206) has about 210Nm of engine torque @ 4500rpm, and a clutch capable of 650Nm. Would a ratio of about 3:1 when it comes to engine vs. clutch capacity be a general one? (I'm just using that to suggest clutch torques to a car builder, and clutches with very high capacity can make the car drive off a little less easy) Thanks, Ruud van Gaal Free car sim : http://www.marketgraph.nl/gallery/racer/ Pencil art : http://www.marketgraph.nl/gallery/

On Tue, 15 Jan 2002 15:46:32 GMT, [email hidden] (Ruud van Gaal) wrote: >Does anybody know how this is solved in real cars? In al cars i had the speed was taken in the out of the gearbox. So if you give full thotlle when the car is in the air the speed does'nt match with the real one. Sebastien TIXIER - Game Developer Dynamics and Car Physics http://www.eden-studios.fr GPLRank Normal:-44.24 Monster:-124.44

On Tue, 15 Jan 2002 16:58:37 +0100, Sebastien Tixier <[email hidden]> wrote:

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>On Tue, 15 Jan 2002 15:46:32 GMT, [email hidden] (Ruud van Gaal) >wrote: > >>Does anybody know how this is solved in real cars? > >In al cars i had the speed was taken in the out of the gearbox. So if >you give full thotlle when the car is in the air the speed does'nt >match with the real one.

Yes it does so here as well (also when braking or accelerating slightly because of slip ratio issues), but for which wheels do you calculate the ratio at which you *think* the car is traveling? I mean, if the front wheels are half as high as the rears (extreme example), and you have 3 diffs, what would be factor be to calculate velocity (in m/s for example) from the gearbox rotation speed? An average of front+rear? Ruud van Gaal Free car sim : http://www.marketgraph.nl/gallery/racer/ Pencil art : http://www.marketgraph.nl/gallery/

Ruud van Gaal <[email hidden]> wrote in message news:[email hidden]... > As I was/am adding a 4WD driveline, I was wondering about deriving > velocity (for the dashboard velocity dial) from the gearbox. My immediate response is to average, having calculated back from wheel velocities. > For a single diff, I can solve the relationship between gearbox speed > (=driveshaft speed) and wheels by the formula: > > perceivedVelocity=gearbox->rotVel*diffRatio*wheelRadius Let's say you have a single diff, driving one large wheel at twice the size of the smaller one opposite. Then assuming straight line travel, [damn! Rice just boiled over] the diff cage is running at the mean of the two wheel rotvels. Taking the wheel road speeds as equal and rearranging, I get roadVel = 2*rotVelDiff * (radiusLarge*radiusSmall) ... ... / (radiusLarge+radiusSmall) You should be able to extend this to include gear ratios in the "radius", and attach a similar formula between two regular diffs. You could even have four different sized wheels, but I think the rearrangement gets a little more, er, interesting! > The problem seems that for more than 1 diff, if the front and rear > have a different 'diffRatio*wheelRadius' product, then depending on > where the torque flows most, you get a different (inaccurate) velocity > dial. It shouldn't depend on torque flow since the velocities have a fixed relationship (until teeth start jumping ;-) Tyre slip will affect the answer, but that's a problem real speedometers have too. > Does anybody know how this is solved in real cars? > I would perhaps guess that the differential ratios in both front and > rear diffs are the same, but that still doesn't account for > differences in wheel radii. I /think/ things are usually arranged to avoid having a speed difference at the centre diff in normal, straight-line driving - it saves wear and tear. Epicyclic diffs can produce a torque split with equal output speeds. > BTW; A small other question for some clutch analysis. It seems my > street car (Peugeot 206) has about 210Nm of engine torque @ 4500rpm, > and a clutch capable of 650Nm. Would a ratio of about 3:1 when it > comes to engine vs. clutch capacity be a general one? (I'm just using > that to suggest clutch torques to a car builder, and clutches with > very high capacity can make the car drive off a little less easy) Sounds *about* right, but I couldn't say more than that. HTH, Jonny

[email hidden] (Ruud van Gaal) writes: > I would perhaps guess that the differential ratios in both front and > rear diffs are the same, but that still doesn't account for > differences in wheel radii. I don't see a problem. you know the ratios and wheel sizes, so just pick an end and multiply. -- Gunnar #31 SUCKS#015 Tupperware MC#002 DoD#0x1B DoDRT#003 DoD:CT#4,8 Kibo�: 2 "Det er nok ingen ovn, men fartsm�leren v�r."

[email hidden] (Ruud van Gaal) writes:

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> On Tue, 15 Jan 2002 16:58:37 +0100, Sebastien Tixier > <[email hidden]> wrote: > > >On Tue, 15 Jan 2002 15:46:32 GMT, [email hidden] (Ruud van Gaal) > >wrote: > > > >>Does anybody know how this is solved in real cars? > > > >In al cars i had the speed was taken in the out of the gearbox. So if > >you give full thotlle when the car is in the air the speed does'nt > >match with the real one. > > Yes it does so here as well (also when braking or accelerating > slightly because of slip ratio issues), but for which wheels do you > calculate the ratio at which you *think* the car is traveling?

pick one. :) > I mean, if the front wheels are half as high as the rears (extreme > example), and you have 3 diffs, what would be factor be to calculate > velocity (in m/s for example) from the gearbox rotation speed? > An average of front+rear? one end. -- Gunnar #31 SUCKS#015 Tupperware MC#002 DoD#0x1B DoDRT#003 DoD:CT#4,8 Kibo�: 2 to err is human -- to forgive is bovine.

Hi

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> As I was/am adding a 4WD driveline, I was wondering about deriving > velocity (for the dashboard velocity dial) from the gearbox > > Suppose you have 3 differentials, a viscous one (center) and 2 other > types in front and rear. If the front diff ratio is different from the > rear diff ratio (where ratio is the inherent gearing ratio from ring > gear to side axles), or if the front and rear wheels have different > radii, how would you derive 'velocity' for your dial? > > For a single diff, I can solve the relationship between gearbox speed > (=driveshaft speed) and wheels by the formula: > > perceivedVelocity=gearbox->rotVel*diffRatio*wheelRadius > > (as rotVel is in radians/sec, the circumference of the wheel, > 2*PI*wheelRadius, falls out and you're left with just the above). > > The problem seems that for more than 1 diff, if the front and rear > have a different 'diffRatio*wheelRadius' product, then depending on > where the torque flows most, you get a different (inaccurate) velocity > dial. > > Does anybody know how this is solved in real cars? > I would perhaps guess that the differential ratios in both front and > rear diffs are the same, but that still doesn't account for > differences in wheel radii.

Well, I think most 4WDs have the same diff ratios and wheel sizes front and rear, if they don't, the overall combination of diff ratio and wheel size will give the same gearing from and rear. So simply take the rpm into (or out of) the centre diff, and multiply buy the (same front an rear overall) ration from there. I think most speedometers are taking from gearbox output speed, ie before the centre diff. If you had a differebt overall ratio front to back this would cause hideous problems, it would destroy your transmission and/or tyres in short order. Of course when you measure speed like this you get the wrong answer with wheelspin, but this happens with real vehicles. Hope this helps. Paul --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.313 / Virus Database: 174 - Release Date: 03/01/02

>Suppose you have 3 differentials, a viscous one (center) and 2 other >types in front and rear. If the front diff ratio is different from the >rear diff ratio (where ratio is the inherent gearing ratio from ring >gear to side axles), or if the front and rear wheels have different >radii, how would you derive 'velocity' for your dial? As the others have said, it seems the combined effective final drive ratio at each end is usually the same or very close to it (tire radius and gear together.) I think I read that Porche used a little different method in order to move the torque split rearwards though.. I planned on doing the speedometer by choosing which end the engine was literally attached to, and using the velocity of that ring gear directly.. Not sure how it works on a real 4WD car though. It seems that you have to hook a speedometer cable to SOME rotating part, so it might as well be the one that the engine is driving... >BTW; A small other question for some clutch analysis. It seems my >street car (Peugeot 206) has about 210Nm of engine torque @ 4500rpm, >and a clutch capable of 650Nm. Would a ratio of about 3:1 when it >comes to engine vs. clutch capacity be a general one? (I'm just using >that to suggest clutch torques to a car builder, and clutches with >very high capacity can make the car drive off a little less easy) Probably a good rule to use, although intuitively I'd think the clutch torque capacity would be closer to the engine torque than this, but we know how good my intuition can be sometimes ;-) I run my clutch usually just 20-40% over the peak engine torque, but that lets there be a bit too much slip it seems when shifing. My gear changes don't actually disengage the clutch yet, so slamming the drivetrain with a 650Nm torque burst during a shift ought to squeak the tires in every gear, something I doubt happens with a Peugeot. Not sure though, just some stuff to think about while deciding... Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com My little car sim screenshots: http://performancesimulations.com/scnshot4.htm

Can this be of help? http://www.apracing.com/car/race/Dynamic.pdf Also.. I'm not sure if that 3:1 ratio sound quite correct... I just had a look thru AP's product range... Their 4-plate sintered Champcar clutch has a torque capacity of 952 Nm... Now i'm no expert on the champcar engines - but a 3:1 ration might sound a bit off to me... Also... are you sure about those figures for you 206? I just looked at the figures for my [soon to be] new car... and it got 149Nm @ 4,500 rpm's.. -- ed_ "Ruud van Gaal" said: > BTW; A small other question for some clutch analysis. It seems my > street car (Peugeot 206) has about 210Nm of engine torque @ 4500rpm, > and a clutch capable of 650Nm. Would a ratio of about 3:1 when it > comes to engine vs. clutch capacity be a general one? (I'm just using > that to suggest clutch torques to a car builder, and clutches with > very high capacity can make the car drive off a little less easy) >

Just wanted to add ath according to Walker Racing, the 2001 Toyota RV8F got "more than 800 bhp" and "more than 300lb.ft" of torque.... That, to me - suggest a ratio closer to 2:1 for these cars/engines.... -- ed_ "Ed Solheim" <[email hidden]> wrote in message news:3c450dfc$[email hidden]... > Can this be of help? > http://www.apracing.com/car/race/Dynamic.pdf > > Also.. I'm not sure if that 3:1 ratio sound quite correct... > > I just had a look thru AP's product range... Their 4-plate sintered > Champcar clutch has a torque capacity of 952 Nm... Now i'm no expert on the > champcar engines - but a 3:1 ration might sound a bit off to me... > > Also... are you sure about those figures for you 206? > I just looked at the figures for my [soon to be] new car... and it got 149Nm > @ 4,500 rpm's.. > > -- > ed_ > > > "Ruud van Gaal" said: > > > BTW; A small other question for some clutch analysis. It seems my > > street car (Peugeot 206) has about 210Nm of engine torque @ 4500rpm, > > and a clutch capable of 650Nm. Would a ratio of about 3:1 when it > > comes to engine vs. clutch capacity be a general one? (I'm just using > > that to suggest clutch torques to a car builder, and clutches with > > very high capacity can make the car drive off a little less easy) > > > > >

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>Yes it does so here as well (also when braking or accelerating >slightly because of slip ratio issues), but for which wheels do you >calculate the ratio at which you *think* the car is traveling? > >I mean, if the front wheels are half as high as the rears (extreme >example), and you have 3 diffs, what would be factor be to calculate >velocity (in m/s for example) from the gearbox rotation speed? >An average of front+rear?

In lot of car the speed is taken between the gearbox and the central differential. In some motorcycle, speed is taken on the rear brake disc. Anyway, i don't think some car takes the speed after the diffs. Sebastien TIXIER - Game Developer Dynamics and Car Physics http://www.eden-studios.fr GPLRank Normal:-44.24 Monster:-124.44

Other point. In rally cars there's a magnetic captor on 1 wheel. Every WRC codriver will tell you that on slippy stages the tripmaster give more km than the real lengh of the stage. Sebastien TIXIER - Game Developer Dynamics and Car Physics http://www.eden-studios.fr GPLRank Normal:-44.24 Monster:-124.44

"Ed Solheim" <[email hidden]> writes: > Just wanted to add ath according to Walker Racing, the 2001 Toyota RV8F got > "more than 800 bhp" and "more than 300lb.ft" of torque.... > > That, to me - suggest a ratio closer to 2:1 for these cars/engines.... I guess that a race engine can do with a lower ratio since it probably has a smaller flywheel / max engine torque ratio compared to a street car. I.e. the flywheel (and the rotating parts of the engine) isn't adding as much torque when starting / speed shifting. _ Mats Lofkvist [email hidden]

On Tue, 15 Jan 2002 19:42:22 -0000, "Jonny Hodgson" <[email hidden]> wrote: First, thanks to all those that replied! >Then assuming straight line travel, [damn! Rice just boiled over] Oops! :) ...

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>roadVel = 2*rotVelDiff * (radiusLarge*radiusSmall) ... > ... / (radiusLarge+radiusSmall) > >You should be able to extend this to include gear ratios in the >"radius", and attach a similar formula between two regular diffs. >You could even have four different sized wheels, but I think the >rearrangement gets a little more, er, interesting!

Hm, yes. Perhaps some iterative algorithm would do better, but I get the point.

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>> The problem seems that for more than 1 diff, if the front and rear >> have a different 'diffRatio*wheelRadius' product, then depending on >> where the torque flows most, you get a different (inaccurate) velocity >> dial. > >It shouldn't depend on torque flow since the velocities have a >fixed relationship (until teeth start jumping ;-)

Well, if you have a VC in the middle and it allows some difference in the frontal and rear feed (which is what a diff does), things can go out of line a bit (but probably give a lot of frictional problems/wear though). The reason I came up with this is someone said a Porsche <x> used a 15/85 central VC diff, so 85% torque goes to the back (under non-slipping conditions, however they define that). So you quickly get more velocity at the rear; but that's spinning basically, so I guess in that case the velocity dial does funny things anyway. And 85% rear is ok during acceleration I guess, since weight is shifted there anyway (so it can take more torque). Thanks, Ruud van Gaal Free car sim : http://www.marketgraph.nl/gallery/racer/ Pencil art : http://www.marketgraph.nl/gallery/

On 16 Jan 2002 03:02:08 GMT, [email hidden] (J. Todd Wasson) wrote: ... > I planned on doing the speedometer by choosing which end the engine was >literally attached to, and using the velocity of that ring gear directly.. Not >sure how it works on a real 4WD car though. It seems that you have to hook a >speedometer cable to SOME rotating part, so it might as well be the one that >the engine is driving... I used the actual velocity before; obviously not right in real cars (although with GPS...). I now take the gearbox, as it's next in my driveline tree behind the engine, and if you have 3 diffs it's a little jungle behind that with respect to gearing ratios. Besides, it seems most cars derive it from the gearbox speed. Also useful to derive the gear sound (frequency) from. > >... 3:1 ratio > Probably a good rule to use, although intuitively I'd think the clutch torque >capacity would be closer to the engine torque than this, but we know how good >my intuition can be sometimes ;-) I run my clutch usually just 20-40% over the >peak engine torque, but that lets there be a bit too much slip it seems when >shifing. It seems so. With much clutch torque it's easier to make donuts from a standstill, with less, you get lots of slipping. I do notice that compared to other cars, the Peugeot 206's clutch seems very grippy, so whenever I lift the clutch pedal it has a noticable grip point which is very hard to get smooth in the lower gears. So personally I'd prefer indeed less capable clutch. > My gear changes don't actually disengage the clutch yet, so slamming >the drivetrain with a 650Nm torque burst during a shift ought to squeak the >tires in every gear, something I doubt happens with a Peugeot. As my car is not too old, I won't test that. ;-) However, I think the sound of the grinding would overpower that from the tire squeak, if you do this in real life. Too bad free shifters with force feedback don't seem to exist yet. :) I'll probably propose a 2:1 ratio, which I think is more fluent than 3:1 (in my real-life experience). Ruud van Gaal Free car sim : http://www.marketgraph.nl/gallery/racer/ Pencil art : http://www.marketgraph.nl/gallery/

On Wed, 16 Jan 2002 06:22:34 +0100, "Ed Solheim" <[email hidden]> wrote: >Can this be of help? >http://www.apracing.com/car/race/Dynamic.pdf Thanks. Interesting page. >Also.. I'm not sure if that 3:1 ratio sound quite correct... > >I just had a look thru AP's product range... Their 4-plate sintered >Champcar clutch has a torque capacity of 952 Nm... Now i'm no expert on the >champcar engines - but a 3:1 ration might sound a bit off to me... I'll go for an estimate of 2:1. >Also... are you sure about those figures for you 206? >I just looked at the figures for my [soon to be] new car... and it got 149Nm >@ 4,500 rpm's.. It has been some time, so it might not be totally accurate. However, I do have the 1.6 16-valve version, which is a bit more powerful than the regular engine (inbetween the normal version and the GTI). Ruud van Gaal Free car sim : http://www.marketgraph.nl/gallery/racer/ Pencil art : http://www.marketgraph.nl/gallery/

On Wed, 16 Jan 2002 23:42:39 GMT, [email hidden] (Eric Cabrol) wrote: >On Wed, 16 Jan 2002 14:19:14 GMT, in rec.autos.simulators >[email hidden] (Ruud van Gaal) wrote:...

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>>It has been some time, so it might not be totally accurate. However, I >>do have the 1.6 16-valve version, which is a bit more powerful than >>the regular engine (inbetween the normal version and the GTI). > > >I thought you had the GTI, because 210 Nm for a 1.6 engine sounds >really _really_ optimistic :-)

You should see the way I drive it! ;-) Perhaps 210Nm is the 'feeling', lol. >For a normally aspirated engine, you can consider that a figure of 110 >Nm / litre is nearly a maximum. Sports motorcycles hardly reach it, >and only a few cars are above 100 Nm/l. >Here are the best data I have : >Ferrari 360 Modena : 104 Nm/l.... Interesting way to look at torque generation. Ok, the P206 number may need to be tuned down then to perhaps 160Nm. Oh let's not estimate; here's a first-hit Google: http://www.theaustralian.news.com.au/common/story_page/0,5744,2246621%255E13232,00.html It says for a 2liter 16v: 194Nm@4100. So that would be 95Nm/l -> 1.6 liter = 152Nm for my car. Ruud van Gaal Free car sim : http://www.marketgraph.nl/gallery/racer/ Pencil art : http://www.marketgraph.nl/gallery/

"Ruud van Gaal" wrote: > It says for a 2liter 16v: 194Nm@4100. So that would be 95Nm/l -> 1.6 > liter = 152Nm for my car. According a spanish site I found the 1.6 16V engine in the 206 Cabrio the engine delivers 110bhp @ 5750rpm and 147Nm @ 4000 rpm's whilch is more in tune with my Cooper which deliver 115bhp and 149 Nm @ 4,500 rpm. -- ed_

On Thu, 17 Jan 2002 15:13:32 +0100, "Ed Solheim" <[email hidden]> wrote:

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>"Ruud van Gaal" wrote: > >> It says for a 2liter 16v: 194Nm@4100. So that would be 95Nm/l -> 1.6 >> liter = 152Nm for my car. > >According a spanish site I found the 1.6 16V engine in the 206 Cabrio the >engine delivers 110bhp @ 5750rpm and 147Nm @ 4000 rpm's whilch is more in >tune with my Cooper which deliver 115bhp and 149 Nm @ 4,500 rpm.

Damn, it gets less all the time. Hope it will even START when I get out of the office tonight! ;-) (otherwise I'll just have to drive home in reverse, lol) Ruud van Gaal Free car sim : http://www.marketgraph.nl/gallery/racer/ Pencil art : http://www.marketgraph.nl/gallery/