Optimal Gear Shift RPM for a Ferrari

It is not the torque at the output of the engine which accelerates the car, but the torque on the wheels.
If you assume that the speed of the car is constant during gear shift, and that the efficiency of the gear box is also constant, then the higher you are on the power curve, the highest torque you have on the wheel : Torque on the wheel = engine power (minus the gear box losses) / wheel speed. For the same wheel speed (constant car speed), the higher the power, the higher the torque, the higher the acceleration.

My vote is for full RPM up to max power ... in addition it is a lot of fun!

 

The other one also ....

In other words, if you have room for a lower gear between the max torque and the max power, you sould select the lower gear for more power and a better acceleration.

 

Acceleration is maximized when the horse power (not TQ) under the curve is the greatest. This means that you should run the car up to redline* and then shift to the next higher gear. The optimal place to shift is when the hourse power prior to the shift is equal to the horsepower power after the shift, with the HP peak pretty close to midway between shifts.

The other way to run this equation is to remember that RWTQ is the TQ of the engine multiplied by the total gear ratio divided by the rolling radius of the rear wheel. Here, you shift upwards when the TQ[RPM] multiplied by the gear ratio in one gear is greater than the TQ[RPM] multiplierd by the next gear ratio. The RPM of the engine after a shift will be RPM[gear-next] = RPM[gear-prev]*ratio-next/ratio-prev.

Plotting either of these with respect to MPH will arrive at the same shift points.

Were the F355/F360 (TQ curves with which I am intimately familiar) engines capable of running to 9,100 RPMs, this would be the ideal point to shift. With the largest area under the HP curve. Alass, given this RPM is out of range, shifting at redline is the best second option.

 

I agree with what you wrote but the end of this sentence. The roling radius is necessary only to compute the force at the tire contact point, not to compute the torque at wheel level.

 

It would seem that maximum torque is reached in each gear from between 3500 and 4500 rpm. Thus, no need to go to maximum RPM, unless you just like doing that.

There have been other threads on what RPM is best for shifting. If I remember, most like the 4000 RPM as it "felt" right. The torque curves would support that.

 

No!
For a given speed of the car, the best acceleration is given by the gear which brings the engine close to its max power, NOT by the gear which brings the engine close to its max torque.

 

You are correct. I didn't state my point very well, heck, it was carp.

What I meant to say was since power is proportional to rpm x torque, when the torque flattens out and no longer increases, the power developed is due only to rpm increase. Thus, at the lower rpm, power increases faster when both rpm and torque increase. The point where power only increases with rpm seems to be the point where many feel they like to shift and get the sporty performance they desire. I know I tend to like shifting in the 3000 to 4000 rpm range. The car accelerates well without the very high rpm.

Does that make more sense?

 

The problem with this statement is that if you are in 3rd gear at (say) 3000 RPMs, you have a certain amount of thrust at the rear wheels. But if you downshift to 2nd or 1st gear you have even more thrust at 4400 RPMs or 5500 RPMs due to the TQ multiplication of the transmission.

But it it time for me to steal this thread to point out something very few realize.

For a car used exclusively for drag racing, having the HP peak occur with a slowly decending TQ curve is optimal. And if you look at some of the TQ curves for typical american V8 'iron' you will see exactly this. This is optimal when the TQ descent has the shape of a 1/x curve and this means that since RPMs are rising, that HP remains at/near its peak for a long time. This is optimal for linear acceleration.

For a car used exclusively for carving corners, the optimal engine characteristics are different. Here, one wants a long flat TQ curve. The reason is that you want the TQ curve flat because you want the suspension to 'take a set' and then accelerate without the 'set' changing. A flat TQ curve does this. The rear end takes its squat and then the car flies around the turn with the rear end not moving either up or down.

Now, if the cornering car is powered by a engine described above like a drag car, the TQ curve is continuing to decrease, this means that the rear end takes its squat, and then as the car accelerates the rear has less and less thrust and therby it slowly raises from this squat. Thus the rear end is constantly changing its set, and the car cannot be setup optimally.

Once the turn is over, one reverts to linear acceleration and the other TQ curve shape becomes optimal again.

 

Yes it does. Your original question was "when to shift". This one is a different story.
If you stay on the same gear, the wheel torque along the RPM range is the image of the engine torque multiplied by the gear ratio. That is what you feel when you accelerate staying on a gear, maximum acceleration is at max torque ... on that particular gear, this is not the max acceleration of the car as discussed before!!! Having the max torque at lower RPM is better for usual driving where you don't want to be too high in RPM for a decent acceleration, and better for fuel economy because the engine has its best efficiency at max torque.

 

As a general rule, I try to stay in the torque band. Torque gets me there, horsepower keeps me there. That's especially true if the course in front takes the car up and down through various gears.

 

The best to shift rpm is different in any gear. You can calculate it if you got a engine torque curve and your gear ratios to calculate with. I wrote a windows programm wich do the job for you and tells you exactly wich rpm in wich gear is the best to change to get maximum torque to the wheels. Ofcorse it could be in some cases better to over rev the gear to get better times on the track if you save a gearchange with that. But for the straight 1/4 mile or something you can calculate it.