Shifting RPM

[Supercharged Vipermad]

I realize this topic has probably been picked over before, but I keep seeing posts of the form "shift early, ~5500 RPM, when your torque is falling off". This is different from my understanding of optimal shifting, which is "maximize your average HP", or in practice, "shift when the HP at your current RPM is no higher than the HP at the RPMs you'll have after shifting."

From inspection my Viper dyno curve, it appears that optimal shift points on a stock Viper is:
1-2 @ 6,200 RPM
2-3 @ 6,100 RPM
3-4 @ 6,000 RPM

Can someone explain the reasoning behind the "shift early" philosophy? It seems to contradict the laws of physics...

 

[Fred(DrivingSchool)Kinder]

What are you trying to accomplish? On a road course the most important issues is car balance and being smooth is the key. The Viper's massive torque has a broad RPM range for good acceleration. Focus on being smooth. Pushing to the fuel shut off will cause more problems than you can gain. It takes less than a second to over rev. when playing in the 6,000 RPM area and then she shuts down.

 

[Tom Welch]

Ben,

I feel your pain with this subject but shifting early will net the best e.t. Heres why. Please note that I am an Pilot and have over 20 years drag racing experience, but I am not an engineer, so laymens terms are common with me.

Your car's powerplant is designed around torque. Torque is what accelerates mass, NOT Horsepower. An example: a 300 hp diesel semi with 600 ft/lbs torque will pull a 40' trailer for hundred of thousands of miles. A small block chevy that makes 600 hp and 480 ft/lbs of torque would not, not to mention it wouldn't last long.

The viper engine has a very broad, somewhat flat torque band that ends at around 4400 rpm's. Your viper engine makes more torque than horsepower by a large margin. BTW, I have yet to see a mildly modified viper that has a horsepower curve that continues to make power past 5500 rpms.

To use only the upper part of the torque band(the result of shifting at higher rpms) is defeating the purpose of the engines massive torque, therefore resulting in less acceleration. Also if power is not increasing after a given rpm, to stay in that gear is netting no gain in acceleration.

If you own a Harley Davidson or small cc dirt bike(yz125 etc) you can test this theory. Get moving in low gear then go WOT the bike will accelerate nicely to a certain rpm, then you will not feel the same acceleration although the motor might continue to rev a little longer, then you will find yourself wide open running along at about 30 mph, shift gears and BANG, here goes that acceleration again, you are back in the power band.

In a nutshell, the power band of a typical viper engine tops at about 5300 rpms(I believe it to be actually lower but because of the cars weight and gearing, shifting at a lower rpm with a stock viper brings the rpms down too low in the torque band in the next gear... with nitrous I generate 620+ RWHP and 700+ rw/ftlbs torque and shift at 4600 rpms because i have the added power to use the ENTIRE torque band)

The best place to test these theories is NOT the dyno but the dragstrip. Try shifting at the RED line, then try bringing the revs down a few hundred at a time until you net the best e.t. Also, you will go faster by shifting into 4th gear in a quarter mile pass instead of running up near the fuel shutoff in third gear at the end of the track.

These are just my opinions backed by my personal experience both on the dyno and over the course of hundreds of quarter mile passes in vipers. I have driven vipers for others and using this method have lowered their best e.t's by up to a half a second.(except for Chris Marshall!!hehehe)

Regards

Tom
Http://btrviper.com

"A bird in the hand is worth 2 in the bush, but if in the bush a fair maiden should stand, a push in the bush is worth 2 in the hand!"

 

[Frank Parise]

Ben, you're definitely on the right track. I love your engineering approach....we need more of you contributing to our learning curve. Been here, done this. See if this helps:

To correct your analysis I believe you have to calculate the cumulative total force (rear wheel torque) throughout the period of acceleration between each gear. In other words, you can't simply look at RWT at the beginning and end of the shift range, or in your first example; 5,600 and 3,745.

Look at your dyno data and compute RWT in 50 or 100 RPM increments between 3745 and 5600 RPM. You may find that it is greater in total than the same figures for a shift range of 4,010 and 6,000.

There is one other very real factor that has been ignored but is really important...the traction limit of your rear tires. They can't handle the maximum RWT that your car will produce, so instead of accelerating your car forward, you will spin tires and go slower.

The calculation of this limitation is dependent about having an accurate friction coefficient to work with. I'd use 1.0 for a perfect set of brand new Michelin Pilots, about 1.3 for a similar set of Hoosiers, and perhaps as high as 2.0 for a good set of slicks. You also need an accurate figure for the weight of your car and the amount of weight transfer that takes place from front to rear. With a 1.0 tire coefficient, you need at least as much vertical force (weight plus aerodynamic downforce) on the rear tires as the RWT produced, otherwise you will spin tires. With a 2.0 coefficient, you only need half the vertical force! Obviously the Hoosier falls somewhere in between.

More complicated, but I know you can do it. Please post your new calculations..I love it.

 

[Supercharged Vipermad]

Frank,
Aaah, I love a good challenge. First off, calculations of weight transfer are not hard once you have the equation, which may be found at: http://www.getfaster.com/Techtips/Physics1.html

Now, my Viper's tires are 335/30-18s, with about 1/2" tread, so they have an effective radius of (335/2.2 * .30 + .5) + (18/2), or 14". This means that rear wheel torque values must be divided by (14/12) to convert from foot/lbs to lbs of accelerative force. Given this, I find that acceleration force maxes out at the following values:
1st gear: 440 ft/lbs * 8.166 * (12/14) = 3,080 lbs acceleration
2nd gear: 440 ft/lbs * 5.46 * (12/14) = 2,060 lbs acceleration
3rd gear: 1505 lbs acceleration
4th gear: 1158 lbs acceleration

A Viper has a curb weight of 3,600 lbs and a 49/51 weight distribution, which means that the rear tires have 1836 lbs of static weight on them. Under max acceleration of .86 Gs, we have 641 lbs of weight transfer, yielding a rear wheel weight of 2478 lbs. By this calculation, the stock rear tires should spin as the motor comes up to full torque around 4,000 RPM, while slicks should stick. However, this contradicts my experience, which is that the rear tires maintain traction once warmed up, even under full acceleration. This lends weight to my budding theory that RWHP in low gears is substantially lower than in higher gears.

Next test: G tech readings in the various gears. I can calculate what the acceleration SHOULD read given gear choice and wind resistance at speeds; I'm curious to see what it ACTUALLY reads. That may help confirm or refute my theory.

>Look at your dyno data and compute RWT in 50 or 100 RPM increments between 3745 and 5600 RPM.
>You may find that it is greater in total than the same figures for a shift range of 4,010 and 6,000.
Actually, I don't need to run the calculation to know it will be lower. Driving power is higher *everywhere* (3000 - 6200 RPM) in 1st gear than it is *anywhere* in 2nd gear, so it MUST be true that integrating RWT through RPM ranges will yield a higher result for 4010 - 6000 than from 3745 - 5600. Similarly, RWT is higher in 2nd gear until 6100 RPM than it is anywhere in 3rd gear, and higher in 3rd gear until 6000 RPM.

Ben "I'm fast, and I've got equations to prove it!" Treynor :^)

 

[BigsViper]

So, In summary you would conclude that.....????

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[Supercharged Vipermad]

Let me simplify, then complicate the question.

Fred: I'm specifically considering drag racing with this question. On a road course the issue is considerably more complicated, and optimal shifting for power purposes really only applies to long straights.

First off, I'm an engineer but not a pilot or experienced drag racer. I believe Tom's empirical evidence that short shifting produces better 1/4 mile times -- I just want to understand *why*. Here's what bothers me:

I think we can all agree that you want to shift when you can accelerate faster in the gear you're shifting INTO than in the gear you're currently in. Now, acceleration is a function of driving force at the rear wheels (F), minus drag and rolling friction, divided by mass. Restated, we have the familiar equation a = F' / M, where F' is the net of driving force minus drag & friction. For the purposes of this discussion, we're trying to figure out optimal shift points, so mass is constant and can be ignored, and drag is a function of speed and tire inflation, and can also be ignored. So the problem is: how to maximize F, the driving force at the rear wheels.

F is simply the engine's torque multiplied by the gear ratios in between the engine and rear wheels. These multipliers are fixed for a given gear, so we can enumerate them:
m1 = 2.66 (1st) * 3.07 (diff) = 8.166
m2 = 1.78 * 3.07 = 5.46
m3 = 1.3 * 3.07 = 3.99
m4 = 1.0 * 3.07 = 3.07

So clearly, optimal shift points occur when the rear wheel driving force (F) in your current gear drops below the driving force obtainable in the next gear. Let's compare shifting at 6,000 RPM with shifting at the HP peak @ 5,600 RPM. I'll use my car's stock dyno graph for these figures, but the basic idea is the same for any car. Note that because I'm using chassis dyno graphs, HP/torque figures are net of drivetrain losses.

At 5,600 RPM in 1st, net engine torque is 360 ft/lbs, which means that driving force is (360 * 8.166 =) 2940 ft/lbs at the rear wheels. Shifting at this point will drop RPMs to 3745, at which point torque is 440 ft/lbs and driving force is (440 * 5.46 =) 2402 ft/lbs.
At 6,000 RPM in 1st, engine torque is 330 ft/lbs and F = 2695 ft/lbs. The shift to 2nd drops RPMs to 4010, at which point torque is also 440 ft/lbs and driving force is also 2402 ft/lbs.
The net of all this math is that the viper is still accelerating faster in 1st at 6,000 RPM than it will when shifted to 2nd. It is thus advantageous to stay in 1st as long as possible, i.e. until redline. I won't repeat the calculations, but the results are similar for 2nd and 3rd gear, except that optimal shifting is at 6,100 in 2nd and 6,000 in 3rd.

So... what's wrong with this logic? Why is it faster to shift early? I can only think of one explanation: the power delivery curve in lower gears looks quite different from the curve in 4th. For instance, in lower gears the mass of the engine & flywheel is much more of a factor, because RPMs are changing more quickly and thus more of the engine's power is being consumed by spinning internals. Also, driveline frictional losses might look different in lower gears -- force in the driveline is higher, so gears will consume more power. Also, only 4th gear is 1:1, so tranny losses will be higher in lower gears.

Two questions for the board, then:
(1) can anyone point out the flaw in my reasoning above?
(2) does anyone have dyno charts for the lower three gears?

 

[Tom Welch]

Wow,

Those are some incredible mathematics. Do your viper "T" shirts have pocket protectors? Just Kidding!

I must add though that both Ben and Frank are leaving out an important factor, which is rolling resistance and the effects of DRAG, both parasitic and aerodynamic that increase exponentionally on the car as it accelerates. These factors work against the powerplant and drivetrain.

Also, I have done dyno tests in both 3rd and 4th gear and have found about a 20 hp and 23 ft/lb torque difference(less power in third gear).

Again, I can only dream of communicating mathematically about the forces of nature and their relationship on the viper, all I can say is the real world testing ground for acceleration is a specific distance traveled in a given period of time. I might suggest that dragstrip testing be accomplished using drag slicks to maximize traction. Use different shift points, making 3 runs at each shift point for comparison and accuracy, find out which set of shift points results in the best elapsed time, then go back and recalculate using the actual numbers.

Might I also suggest purchasing from any dodge dealer the Mopar Chassis Tuners Guide. It has several drag strip formulas in it that have been used by Mopar and the other OEM's for decades. I have used them on all of my cars including my viper. If you know 2 simple items, 1) the cars weight with driver and 2) your trap speed in a quarter mile run, your rear wheel horsepower and torque can be factored. NOTE: Runs must be made either on the same day or in similiar weather conditions for optimum results.

Good luck,

tom

 

[Supercharged Vipermad]

Pocket protectors, pshaw! Professional practitioners of performance persuits prefer Palm Pilots.

I did go out last night and perform some tests with my G-Tech. I saw maximum acceleration of .77G in 1st gear, .59G in 2nd gear, and .45G in third gear. Acceleration would drop off above 5,000 RPM, just as you'd expect from the torque curve, but I could not tell whether it dropped below the available figure in the next higher gear -- there were a lot of cops out last night

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I'm certainly going to follow Tom's suggestion of trying various shift points next time I'm at the dragstrip. I'll do one set of runs shifting at 6200 / 6100 / 6000, and another shifting consistently at 5800 RPM. I'll certainly post my results. Tom, any donations of rear wheels with drag slicks (for the sake of science, of course) would be graciously accepted

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[Supercharged Vipermad]

After taking my car to the dyno, I quickly did the cheap and dirty calculations (Torque * gear ratio) to figure shift points without any other calculations. On motor (410HP/480tq) the shift points were 6200,6100,5800 and on nitrous (530/710) the shift points were about 650 rpm lower. I really thought this would help on the strip.

Here's what I noticed at the track (nitrous only). My best times happened when I shifted at about 4700 rpm as suggested by Tom Welch and Doug Levin. One thing that truly stuck out was that shifting 1-2 on nitrous at 4700 my street tires were spinning out of control. The higher I went in RPM the less wheel spin I encountered. Can anyone explain this to me?

For another thing - how accurate are our tachs?

 

[Tom Welch]

Dave,

You spun harder shifting at 4700 rpm because you were still solidly in the power band with the cars mass not accelerating fowrard enough to overcome the gearing. At higher rpm you were out of both the power band and torque band along with the car not accelerating as hard at that rpm. I suggest "granny" shifting at least the 1-2 on street tires to prevent excessive wheelspin. USE THE TORQUE, Luke!.

Take care,

tom