Gearing for Top Speed

[hcoles]

I'll move this to the off topic section if people don't like it here. I'm asked to do some "engineering" type analysis as needed for a Bonneville car.

There are many smart people here with a wide variety of automotive design knowledge and experience, so I post here to start with. Maybe best for interested parties to gather OT or use PM.

Problem - Top Speed Final Drive Gearing Selection for Bonneville Streamliner.

What are peoples thoughts? What are the important inputs?

I can post the engine curve and can estimate a total resistance curve.

Motor = Suzuki 750cc GSXR mostly stock - I have the gearing info. I estimate the output at 125HP@13,200rpm at the rear tire on a motorcycle per dyno runs found on the internet.

We ran 223mph a few weeks ago at Bonneville.

We may want to gear to get the next record not necessarily for a maximum.

The course is 5 miles, the speed is trapped for miles 3, 4, 5. I think that is the case I still need to confirm. The rule book is difficult to interpret in spots.

So far it seems the traction is good, we don't hear that the tire is slipping and the tire is showing very little wear. Some cars put down black marks.

It doesn't take long to get through the first 5 gears and into 6th. I should confirm this with the driver. I don't have time or distance series data on speed, that would help of course. I'm lobbying for a data collection system.

I'm hoping this doesn't get into a torque vs. hp tread, the analysis should resolve that IMO.

[javadog]

I can help out. Post the info that you have for the power curve, resistance and gearing. Give me the details on the motor (year, fuel used, any modifications). Let me know whether you were still accelerating when the speed was measured and what the tach readings were. Have you verified that the tach is accurate? I also need an idea of where you reached top speed on the course and where the future timing will be taken.

JR

[hcoles]

JR,
Thanks for the reply. Please stand by I'll pull some graphs together and see what the driver can remember. The tach is a display in front of the driver from the Power Commander V Dyno Jet system. I think we can assume accurate rpm readings, what the driver remembers accurately is another question. He is very busy and concentrated on keeping the car on the track and not missing the mile markers for shutdown/pulling the shute/etc. He says he is hitting the rev. limiter or very close during shifts. I tried to find out what that (rev. limiter setting) is, but so far can't. I got the engine model number, the dealer couldn't translate, said to all Suzuki and confirm the engine, this confirms the internal trans. gearing. It (rev. limit) might be around 14.5k rpm. The Power Commander V map stops at 14.5. Not sure this indicates much. I need to pull this together better for you. Humans are poor data collectors. Thanks for the help.
-Henry

[javadog]

Henry,

Shoot me a picture of the engine and I'll tell you where to look for the type number.

JR

[hcoles]

On engine case - R745 110394
might be a 750 GSXR 2007 motor but that is what I'm trying to confirm.
Our chain drive was 17 driving 30 for the 223mph run.
The chain is a 520 which I have some issue with should be 530.
I calculate the 17 tooth was spinning at ~6k rpm at top speed, but I need to calculate this again.

Thx.

[Flieger]

Well, if you knew the precise drag coefficient, the drag force is cv^2, and set that equal to the thrust, which is torque divided by the tire radius (at speed with the centrifugal force expansion). v is rpm times tire radius. (keep in mind you need to work in engineering units like hz, ft, lbf, slugs, seconds etc). So the torque you use is the torque you make at the rpm for that speed.

cv^2=[(hp)/(v/r)]/r

cv^2=[(hp)r]/(vr)

cv^2=(hp)/v

cv^3=hp

you end up with something like this:

v=[(hp)/c]^(1/3)

Which gives the maximum speed you can reach for a given hp. You look at your peak hp rpm and gear the car to do the speed you came up with in the formula.

The problem is there are other factors of drag that vary with speed such as rolling resistance which will knock the practical top speed down, so you should allow a fudge factor there.

That formula above does not correct the units. But you can take the general idea and just add the conversion factors for things like horsepower and rpm.

[hcoles]

@ Flieger,
Thanks that's approx. what I was thinking, I'll do some initial passes to get the units/etc. figured out and post a graph/equation that should be the tire force on the ground as a function of speed in 6th with assumptions listed. Then work on the other curve of resistance as a function of speed. Where the two cross is the top speed possible given unlimited space. I'm thinking that at these speeds the weight of the car and inertia of the wheels/etc. can be left out of the picture. I'll need to do a check on that. Driver indicates not much acceleration was happening during the mile of record. All is a bit hard to track down.
Thx again.

[Flieger]

You could measure top speed in say second or third gear and work out a correction factor to fudge the "c" from aerodynamic drag, and thereby lump all the v^2 resistance terms together.

Horsepower = (33000lbf*ft/min) and the hp numbers are gotten by torque(lb-ft)*rpm/5252

You need everything as pounds force, feet, seconds, Hz or else everything in newtons, meters, seconds, Hz

rpm/60 = Hz

You also need to work on the rpm drops between gears so that you can accelerate to the highest speed possible in your timed section. That is what makes this more interesting since the space is finite, rather than just going for Vmax.

[hcoles]

OK, here is a data dump.
engine is a 2008 GSXR 750, I called the cus. service line to confirm, dealer not able to confirm

Here is a typical dyno chart - trend line HP, then able to convert to torque and/or use other places



Here is tractive force available vs. vehicle speed, I think this shows no reason to shift early, the GSXR is designed to rev. looks like shifting at 14k or at rev. limiter gives best acceleration times. Lines end at 13.5k rpm shown in tractive vs. rpm chart. Conversion using:
ratio between engine and transmission
transmission ratios (6 speed)
final chain drive ratio (this is what we can adjust, currently 17/30)
tire rollout (growth not confirmed but reported to be 1"r at 230mph)




For a slightly different look for reference, here is tractive force available vs engine speed

[5String43]

To figure gearing, would you also not need the effective dynamic circumference of the rear tire? Surely it grows some at speed, even if it's only a little.

[hcoles]

Yes, as mentioned the current analysis assumes zero growth, I'm in the process of finding that info to make the required corrections.

[Flieger]

Looking at this from an elapsed time perspective (since you are timed over three miles rather than just the highest instantaneous speed), you should have closer gear ratios. Are you allowed a push truck?

You want the thrust vs. speed traces in each gear to intersect so that the thrust and speed in the lower gear equals the thrust and speed in the higher gear, but so that you are now on the rising part of the line for the higher gear.

This will result in the best acceleration, which will ultimately give you the best time and so the best average speed, although the shear length of the track may mean you can hit your theoretical Vmax before the 3rd mile without the closer gear ratios.

That is a nice torque curve.

Looks like the peak hp is about 125hp at 13000rpm.

Now if you can do some coast-down testing you can get an idea of the total drag and therefore get a good estimate of the c value in the formula, then plug in and find the theoretical Vmax and gear 6th for that using 125hp at 13000rpm. Then spread the gears back down to first so that you can maintain good acceleration. If first is too long you need to either get a push or compromise on 6th gear (make it lower, reducing Vmax but gaining acceleration and so improving the measured average speed).

[hcoles]

Yes, a push truck is used, as soon as first gear is engaged, the car is gone. Not sure when this happens but very soon after the start certainly before the first 1/2 or 1/4 mile. I think the trap speed for the record is over any of the 3 or 4 timed miles. I'm still confirming exactly how this works. My chart shows as you say when to shift, stay in lower gear until you hit the next line, this is where the thrust hand off is. The transmission gears can't be changed without extreme extra cost. It looks like to me the 4-5-6 gear spacing is pretty good, I expect the Suzuki engineering people put considerable thought/testing on this. Coast down, yes that is what we need and what we don't have. I can only estimate Cd for the drag line to hit 223mph. That's what I added on this chart below. The car has a very small projected area.

Maybe next I need to estimate speed as a function of track position, this is of course really what we want to know. I need to see if I can do this without using VBA. I'll need to put something in for inertia.

[Flieger]

If you can find a long tunnel like Laurel Hill or other straight road sheltered by trees from wind it would be good to do some coast down testing. Just measure the distance from pulling the clutch lever in until the thing stops on its own, then use some math to find the Cd*A incorporating aerodynamic and mechanical drag.

I am used to seeing gear charts that overlap. That is better for acceleration, and this is effect a type of drag race, going for ET.

So if you can only change final drive I would just gear for Vmax.

[Walt Fricke]

Max is right in that track cars always have overlaps (except perhaps for 1st to 2d) in the thrust per gear vs speed charts.

Can you spin this motor to an even higher RPM without damage to it? That would be another way to have those curves cross each other. Without crossing you are losing a sort of triangular area under the curve as you accelerate through the gears.

It is a shame you can't change the gearing, though. Using the formulae, leavened with some empirical testing, there ought to be an optimum top gear - one in which the drag at your top speed just equals your peak horsepower, with a top gear selected to make that happen.

Perhaps you could change rear tire diameters a little, if your top gear proves to be too tall? Or increase it if too short?

[hcoles]

I'm interested to see if I change the spread sheet entries produce results as you guys mention, where the force available in each gear overlaps the next gear. I assume the Suzuki people know this. Or maybe my analysis has some error.
The driver says he shifts much higher than 13 so we may already be shifting at the overlap, I just didn't find a dyno run with data that high. Gears 4,5,6 seem pretty close. Are you suggesting that tighter gearing will give better results, maybe it will but maybe the final drive ratio needs to be optimized first. It is much cheaper to change.

As a side note - I don't like the roller chain stresses I see - another subject. I probably need to move this discussion to the salt flats forum because it doesn't contain much Porsche content.

Also, not sure how much we lose if not shifting at the exact perfect rpm, the track may be long enough to make up for it or we are only talking 1-2 mph of top speed difference.

I now have the timing slip data from three runs. I'm working on confirming exactly what the mph numbers mean (what are the exact timing light locations).

[Flieger]

The Hyabusa is a sports-tourer. Can you swap the GSX-R 1000 ratios into the 'Busa? Being a proper sport bike, the ratios should be closer for better acceleration, which you will need since the speed is measured as time over 3 miles, if I understand correctly. Then you can just tweak the final drive for the theoretical Vmax you calculate from the formula once you get some coast-down testing done. A 750 Gixxer might have even closer ratios due to the smaller motor, in case the 1000's aren't any better.

[hcoles]

Originally Posted by Flieger

Well, if you knew the precise drag coefficient, the drag force is cv^2, and set that equal to the thrust, which is torque divided by the tire radius (at speed with the centrifugal force expansion). v is rpm times tire radius. (keep in mind you need to work in engineering units like hz, ft, lbf, slugs, seconds etc). So the torque you use is the torque you make at the rpm for that speed.

cv^2=[(hp)/(v/r)]/r

cv^2=[(hp)r]/(vr)

cv^2=(hp)/v

cv^3=hp

you end up with something like this:

v=[(hp)/c]^(1/3)

Which gives the maximum speed you can reach for a given hp. You look at your peak hp rpm and gear the car to do the speed you came up with in the formula.

The problem is there are other factors of drag that vary with speed such as rolling resistance which will knock the practical top speed down, so you should allow a fudge factor there.

That formula above does not correct the units. But you can take the general idea and just add the conversion factors for things like horsepower and rpm.

I'm going to look at this again...I don't think I've put this down yet. The max HP should connect with the drag HP to get the fastest speed. As you indicate this is a cubic function once Cd*A is estimated. Of course there are a number of other factors such as inertia/etc. that many account for discrepancies, perfect gearing which probably can't be achieved, or in infinitely long course. Right? Thanks for the comments.

[Flieger]

The inertia and finite course length are taken care of by having multiple ratios with proper spacing. You want to have most area under the thrust vs distance graph (which is not the same as the thrust versus speed graph). You do this by keeping the engine up near peak power at all times and having the right number of ratios so that you do not loose time by interrupting power during a huge number of shifts but not so few that the engine has to rev considerably outside its powerband. If the power curve is flat and broad you can get away with fewer ratios and fewer gearchanges, which is good. Motorcycles usually have instant upshifts. BMW and others have those quick shifters where it is like an F1 car where you don't even lift the throttle, just bang the gears.

Things that are not taking into account are wheel spin and the other sources of mechanical resistance, but that mechanical drag can be lumped into the aero drag with coast-down testing. You won't get an accurate Cd*A number, but you don't really care about that for your top speed. You get the more valuable term of total drag.

[hcoles]

I might not have mentioned, our mill is a 2008 750 Gixxer. The course has a two mile entry area, then 3 miles are timed separately. So we get two miles to get into top gear/etc. As you get going the miles don't take long to pass over. E.g. ~15 seconds. In other words we get 4 miles to accelerate before entering the last timed mile.