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# racing tranny2

## racing tranny

(OP)
It's often said that the moment of inertia of the transmission is very important to a light, racing car. So important that shaving a pound off the transmission rotating part is going to do more good than shaving a pound off the vehicle body. Can someone explain? Is it really significant? I think there is also a formula that relates all this, and it has a lot to do with the gear ratios.

Another thing I've noticed is that a lot of racing cars and motorcycles have gear ratios that are very closely spaced. For example, a lot of those Japanese road bikes may have a 5 speed transmission with a overall ratio span less than 3 or 2.5. (if you divide the tallest gear by the shortest, they are usually less than 3). Why is this?

Does anyone know the gear span (and ratios if possible) of a typical F1 car or Rally car?

Thanks

### RE: racing tranny

Reducing the weight of rotating components is almost always better than reducing the weight of static components, because you then have a smaller rotational and translational inertia to accelerate.

The formula is pretty obvious if you use an energy method.

You should be able to work out the ratios of an F1 box, and its span, if you can find a trace of RPM over a lap.

eg

http://members.optusnet.com.au/greglocock/cepstrum.htm

Williams and Renault may have better traces on their F1 sites.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

### RE: racing tranny

"Another thing I've noticed is that a lot of racing cars and motorcycles have gear ratios that are very closely spaced. For example, a lot of those Japanese road bikes may have a 5 speed transmission with a overall ratio span less than 3 or 2.5. (if you divide the tallest gear by the shortest, they are usually less than 3). Why is this?"

With high power-to-weight ratios, they don't need real low gears (generally). But such engines usually don't have real flat torque curves, so having many closly-spaced gears helps keep the revs where they belong.  Notice how "good" trans. have the higher gears much more closely spaced than the lower ones-a point usually ignored by Detroit for their "commoner" cars.

Also, while any weight reduction is beneficial, esp. rotating weight, the difference to the engine while accelerating in gear is just about zero.

### RE: racing tranny

(OP)
"Also, while any weight reduction is beneficial, esp. rotating weight, the difference to the engine while accelerating in gear is just about zero."

Can you explain the last part further? You mean it's only beneficial while shifting?

### RE: racing tranny

When an engine is accelerating a car/bike, the rate of RPM increase is so slow (relatively) that the weight of flywheels and gears doesn't mean much.  On dirt bikes where the rear wheel can easily spin and lose traction, a heavy flywheel can slow the spin-up and keep better traction.

The revs can change very fast during shifting, so gear/clutch-plate weight can have a big influence, but once the engine is hooked up to the load it's all slow-motion from a spin-up POV-especially in the higher gears.

### RE: racing tranny

Referred rotational inertia of the engine and driveline is about 25% of the vehicle's mass, in first gear.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

### RE: racing tranny

In my opinion, reducing rotational weight in the engine, especially the flywheel (because of it's large diameter), makes a significant difference. Further down the drive line, the emphasis reduces with gearing and therefore rate of speed change. Despite this, I also think that the wheels play a significant part as even though the rate of rpm change is at the slowest part of the drive train, the weight and diameter are significant.

A weight saving any were in the drive train still has a larger influence than a similar weight saving on the chassis.

Even the smallest saving should be exploited in racing, but if budget dictates, spend the available money on the drive train.

Regards

eng-tips, by professional engineers for professional engineers
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

### RE: racing tranny

Can't argue with that that... but bear in mind that it is an N^2 relationship, so once you are out of first gear then engine inertia matters less and less. Also, it is far easier to pull a couple of kg out of the body than 0.5 kg (or whatever) out of an engine.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

### RE: racing tranny

(OP)
I'm trying to calculate the rotational inertia involved in a racing vehicle.

Can someone give me an idea of the diameter and width of the gears (an average) in a

F1 car
a Rally car

Thanks.

### RE: racing tranny

Pat, I know this is not necessarily relevant to drag racing, but let's not forget that the ultra light drive train is  felt mostly in top gear on 'deceleration'. An engine with a light flywheel will rev much quicker than an equal engine with a heavy flywheel under no load conditions, but the effect is rather diminished in top gear. Now, on the other hand, under heavy deceleration, the light flywheel engined vehicle is at advantage.  I know I don't use the engine exclusively for braking, but it still is a factor, and oft times, a big factor...particularly when braking where no gearchange is needed.

Greg, I try to make the drive train a  light as is practical because in most class racing, a vehicle weight limit is in effect.  My problem is with the idiot that drives my car.  He has gotten totally FAT in his old age.

Rod

Rod

### RE: racing tranny

Greg,
"Referred rotational inertia of the engine and driveline is about 25% of the vehicle's mass, in first gear."

Where did you get that from?  I won't say it's impossible, but it's hardly a "normal" % with common 1st gear ratios and flywheel/gear train weights/inertias.

You'd need very heavy inertia and very low 1st gear to have such a high %.

### RE: racing tranny

To the original poster---   www.taylor-race.com

Rod

### RE: racing tranny

Metalguy

That's a rule of thumb number from many years ago when I was first working in the area of performance prediction.

Reasons why it might be right (1) the guy who told me to use it was a brilliant and thorough engineer (2) the extreme difficulty cars have in getting 0-60 times under 3 seconds. 3) full throttle no load accel time for an engine is 1 or 2 seconds

Let's do it the hard way. mass of crank is about 40 kg, arm is about 0.05 m, so I is 0.1 kg m^2

overall gear ratio is about 10, so that's 10 kg m^2 at the wheel. rolling radius is 0.3,so that's about 100 kg of referred inertia

I'm happy enough that it is in the ball park, given that I've ignored a lot of the other components, especially the flywheel and clutch.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

### RE: racing tranny

Was searching for a specific inertia value and Google brought up this old thread. I realize this site is supposed to be for engineers, but I also realize that a lot of non-engineers come here for help, so, Greg, I hope you don't mind if I "translate" your calculations into something more recognizable to the American motorsports enthusiast.

Greg refers to an inertia of 0.1 Kg-m^2. If you multiply this by 3417, you get the inertia in lbm-in^2.

Multiplying a tire radius of 0.3 meters by 39.37 will give you the radius in inches.

Finally, that which is often called the "equivalent mass" is found by multiplying the inertia and the square of the overall gearing and then dividing by the square of the tire radius. Using Greg's figures, this would be:

(341.7)(10)^2/(11.81)^2 = 245 lbm

(Don't let the "lbm" throw you. The numerical value is the same as the "lbf" or, simply, weight.)

This equivalent mass is the extra mass (weight) equivalent of the effect of the rotating inertia.

I thought this translation might be helpful, Greg, since all that metric stuff just doesn't fly here. The government tried to force it on us a few years ago, but we're a rebellious lot. And, no, I'm not trying to "change" anybody. Years ago, I was one of those who thought it made much more sense to slash "O's" instead of "zeros," and I ended up on the losing side, so I've learned to live with such things.

### RE: racing tranny

I cut and pasted this from my Excel program. The columns don't exactly line up here, but you can see the difference in equiv. wts. by changing the flywheel wt. by one lb. (from 9 lbs. to 10 lbs.) and the effect in each gear.

Setup 1 Setup 2
Flywheel Weight (lb)    Wf =             9        10
Flywheel Radius (in)    Rf =             5        5
1 st Gear Ratio    1 =                   3.19              3.19
2nd Gear Ratio    2 =                   2.22          2.22
3rd Gear Ratio    3 =                    1.6        1.6
4th Gear Ratio    4 =                    1.29           1.29
5th Gear Ratio    5 =                     1             1
Final Drive Ratio    FD =             5.57           5.57
Tire Radius (in)    Rt =              13             13

Equivalent Weight 1st gear (lb)    We1 =    210        234
Equivalent Weight 2nd gear (lb)    We2 =    102        113
Equivalent Weight 3rd gear (lb)    We3 =    53        59
Equivalent Weight 4th gear (lb)    We4 =    34        38
Equivalent Weight 5th gear (lb)    We5 =    21        23

So, as you can see there is a distinct difference even in high gear.

I hope this helps.

Greenlight

### RE: racing tranny

One other point re inertia of rotating components.

It seems so simple that it seems offencive to mention it, but I haven't seen anyone take the normal or linear inertia of rotating components during acceleration as well the rotating inertia.

Regards

eng-tips, by professional engineers for professional engineers
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

### RE: racing tranny

Greenlight,
Try this.  You're at Bonneville in your not-so-aerodynamic car/truck.  Your little 2 liter engine can turn 12,000 RPM, and you're in high gear approaching top speed.  It takes ~5 seconds to go from 11,000 to 12,000.  The engine doesn't  feel a 2 lb. wheel vs a 10 lb. one.

I have an old LP record of "Sounds of Bonneville".  Blown hemi has a clutch problem.  It holds until the torque reaches some level.  You can hear the engine pulling the car slowly up to speed, and when the clutch slips the engine revs skyrocket instantly-far less than a second.

My AA/FC had a very heavy triple disk Crowerglide.  Throttle response in neutral on a blown fuel engine is *immediate*, even with a heavy flywheel/clutch.

Now, where does your formula account for engine RPM rate of increase?

### RE: racing tranny

Working backwards from Greenlight's figures and assuming 350 foot-pounds available from an engine that is no longer attached to the rear wheels, that means an acceleration of around 13,000 rad/second2. Yes, that's pretty instantaneous and it's exactly what Greenlight's equations would predict.

And, Pat, wouldn't the weight of the rotating components be included in the total car weight? Are you suggesting they should be separated? Why?

### RE: racing tranny

No

I am suggesting that it has a double effect.

A pound off the flywheel is a pound off the car, and has that benefit as well as a pound of the rotating mass, so it also has that benefit. a pound off the car is only an advantage in the first instant.

After reading the above sentence, I now realise why grammar was never a good subject for me.

Regards

eng-tips, by professional engineers for professional engineers
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

### RE: racing tranny

Okay, Pat. I hadn't been thinking in terms of "deltas," so your comment threw me.

Just noticed that reference to "fora." Someone took high school Latin! Was watching a documentary the other day on college bands and their halftime performances. The documentary was probably made back in the fifties. They referred to "football stadia around the country." Had to laugh. I came out of retirement to teach at a private Christian high school for a year and the kids are so dumbed down now that only a very, VERY small percentage of their generation would ever understand that. I once made reference to turn "apices" in a hotrodding forum post and that resulted in some curious responses.

### RE: racing tranny

[Quote] Metalguy said "My AA/FC had a very heavy triple disk Crowerglide.  Throttle response in neutral on a blown fuel engine is *immediate*, even with a heavy flywheel/clutch.

Now, where does your formula account for engine RPM rate of increase?" [Quote]

Whenever I am trying to grasp a concept I try to look at the problem at the extremes (often exaggerated extremes).

Rev the engine without a flywheel attached from idle to 8,000 (or whatever rpm is your max).

Next, attach a 200" diameter, 5" thick, solid steel flywheel to the engine and rev it from idle to 8,000 rpm.

Now you can easily get the picture.

Remember, inertia is to angular coordinates as mass is to linear coordinates.

Try lifting a mass of 1kg quickly (say 0.1 sec) from a height of one meter to a height of two meters. Now try lifting 5kg just as quickly. It takes more force to do it.

Now try rotating a 1kg, .4m dia., aluminum disc from zero rpm to 5000 rpm in 0.1 sec and repeat with a 5kg, .4m dia., steel disc. The heavier disc will require more torque.

It's easy to say the "heavy" Crowerglide rev'ed "instantly", but if you measured the time in milliseconds you would easily see the lightweight clutch (lower inertia) would rev a quicker "instantly". The heavy Crowerglide was likely not so heavy when you compare it to the crankshaft, balancer, pulleys, frictional losses of the pistons, etc. which also had to rev "instantly".

The example I presented of the 9 and 10 lb flywheel and the equivalent weights should give you an idea of how much quicker your car, boat, airplane, etc. will accelerate. If you car weighs 5000 lbs., then the 24 lbs. of equiv. wt. won't make much difference. But if you car weighs 960 lbs. (as does my dragster, total wt. including the driver) the 23 lbs. of equiv. wt. in first gear makes about .02 sec. in the first 60 ft.

I hope this helps you envision the affect of lower inertia.

Regards,

Greenlight

### RE: racing tranny

Another way to look at it is in the operation of an Inertial Dyno.  All the engine is accelerating is the flywheel.
I can vary the accel rates from idle to max needed rpm from 2 secs to 6 or 7 seconds just by adding a heavier flywheel.

Ken

### RE: racing tranny

Greenlight

What I have a problem with is that engines usually don't accelerate at constant rates.  Once past the torque peak the rate slows down, assuming a constant load.  In real life that load is constantly increasing, so how can your figures show a simple weight equiv. no.?  My example with the Bonneville car was to show just how slow the high gear accel. can be.  Flywheel effect is lower as the rpm increase slows down.  This is elementary.

Take your super light dragster.  What RPMs did you use for launch (0 speed) and for 60' speed? How many seconds?

Lighter flywheel, etc. are almost always good, but the effect diminishes with each higher gear (as has been well noted), and also with other factors, so a single number doesn't do it.

### RE: racing tranny

Once you start to worry about the applicability of an approximate correlation factor you need to go back and rewrite your acceleration formulae in terms of F=M*a plus several cases of T=I*alpha where relations do exist between a and the various alphas.

Norm

### RE: racing tranny

#### Quote:

It's often said that the moment of inertia of the transmission is very important to a light, racing car. So important that shaving a pound off the transmission rotating part is going to do more good than shaving a pound off the vehicle body.
An important piece of this question is where the weight is being reduced. Rotating mass in general is more "important" pound for pound than body weight. However the rotating mass of  any transmission internals that are not mechanicly part of the output shaft are the most important. The less mass in the clutch disk, input shaft and intermediate shaft the faster you can shift and the smaller your synchros can be (if you have them). The faster you shift the more time you are puitting power to the ground.

As an added bonus weight out of this part of the transmission is still taken off of the total rotating mass and the body mass.

### RE: racing tranny

Would a 10lb, 8in. dia. flywheel accelerate faster than a
10lb 14in dia. flywheel given the same input?

Kevin

### RE: racing tranny

Rotational moment of inertia is an integral involving mass*radius^2, so in most cases the answer would be "yes".  But you could contrive a combination with severely skewed radial mass distributions in which the opposite would be true.

Norm

### RE: racing tranny

I'm with metal guy being ex AA/FC driver. Even back in the mid 70's you would never get the pedal to the floor before the engine blew believe me. The throttle response of a blown fuel motor is rediculous.  Look at it another way. Assuming the blown alcohol motor motor produces 3000 hp at wide open throttle and torque and hp cross at 5250 rpm even at 2500 rpm idle going to WOT in .1 sec (slow) the crank rods pistons flywheel and clutch only weigh 200 pounds and you probably have at least 2000 hp and resulting torque all trying to rotate a measley 200 pounds up to speed. It doesn't make one iota difference here 5 pounds 10 pounds. What counts is how strong is everthing. It's said that the crankshaft on today's top fuel motors can twist up to 20 degrees. I'd have to see it myself but a lot of onboard research has been done on this stuff.
I don't remember what the Crowerglide weighed but a complete 3 disc was one you didn't want to pack around very far. Probably 35 pounds with aluminum flywheel.  We went from an aluminum flywheel to a 1" solid steel flywheel and went quicker and faster no other changes.
In really old days it wasn't uncommon to have 60-70 pound flywheels on a 283 Chev. This is a small hp motor and very high reving. They would buzz them to 9500 on the line and drop the clutch.  The inertia of the flywheel plus the still added hp would launch the car like a shotput. It was how fast you could row the gears that mattered. The motor hardly changed speed at all. As noted close ratio transmissions ruled the roost with this set up.

### RE: racing tranny

#### Quote:

Can't argue with that that... but bear in mind that it is an N^2 relationship, so once you are out of first gear then engine inertia matters less and less. Also, it is far easier to pull a couple of kg out of the body than 0.5 kg (or whatever) out of an engine.

True, but it's really easy to shave a pound off your wheels--at least from stock. A stock car often has wheels approaching or exceeding 20 lbs, most which is at the circumference. Aftermarket aluminum alloy wheels (or magnesium) can usually be less than 10 lbs (heavily dependent on size). This can affect performance in easily noticeable ways--and not just acceleration but also handling as the unsprung mass is reduced.

### RE: racing tranny

It reduces power needed to accelerate the drive line.  It has most effect in 1st, less in 2nd gear ratio, not a lot in 3rd and nearly no effect in top or overdrive.  It has no effect on constant speed running as drivetrain is not accelerating.  It has most effect on fast running parts like the engine flywheel and less on slow parts like wheels.

If you have enough power to spin the wheels in 1st and 2nd any  effective increase in power will just spin the wheels faster and may cause wheel spin in 3rd as well.  BMW F1 1500cc M13 turbo had enough power to spin the wheels in 4th.

If you don't have enough power to spin the wheels or wheelie in 1st, then a reduction in flywheel mass may help achieve this.  The driveablity issues this brings may actually reduce 0-60mph times, impact 1/4 mile times and will give poor engine feel in normal road use, with very rapid drop in engine rpm between gear changes and lack of inertia resulting in a tendency to stall easily.

Conclusion.
It has little use and would be a waste of time and money removing mass from rotating parts on FWD vehicles that can wheelspin anyway.  Just makes more expensive tyre smoke, quicker.
It has no useful effect on modern powerful tunned RWD cars that can wheelspin in 1st and 2nd (or higher gears). Just makes yet more expensive tyre smoke.
It's only effective for AWD/RWD cars that can't wheelspin in 1st with rules, regulations or laws that prevent the addition of proper power adders like turbocharger, supercharger or nitrous oxide, all of which work just as well in top gear as 1st.  In fact they work so well in 1st that they often reduce the power added in 1st by reduced boost or staged nitrous to avoid making expensive tyre smoke.  So that really means racing of vintage or classic vehicles from a time when it was a part of the tuners normal methods.  (It's time for "professional" tuners to wake up, get smart, learn a bit of physics and move on)

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