PSI Setup Tutorial Part 9 - How to setup a gearbox

Hi Racers,

its time for the PSI Setup Tutorial Part 9 - How to setup a gearbox.

Prewarning:
This is a very technical post. Its needed to get behind the truth of gearsettings. Don’t feel frustrated when you come to the point where many questions rise up. Just ask under comments here or on the G+ Website. I come back to you as fast as possible. 


Ok lets start.
What does that mean setting up a gearbox? In most cases it means changing the gear ratio in a way  that allows your car to accelerate as fast as possible without over-revving your engine. Wow thats simple, we just need to make sure the engine reaches maximum revs torwards the end of the longest straight on the circuit. Indeed many simracers only do that. They set their 7th gear ratio that it fits the fastest achievable speed on a circuit.

But what are we doing with the other 6 gears a 7-gear transmission provides? Is it good to let the first 6 gears on standard settings and only adjust the last gear?

Lets further investigate what a gear ratio really is.
A gear ratio indicates the number of revolutions a motor has to do for the driving wheel to complete one full revolution. So for example a ratio of 2.0 means that when the motor has done 2 complete rotations, the driving wheel will have done just one. A higher number means a smaller ratio and conversely a smaller number means a higher ratio.
Again think about it:
Ratio 2.0: The motor has to do 2 rotations for the driving wheel to do one.
Ratio 9.0: The motor has to do 9 rotations for the driving wheel to do one.
Its pretty obvious that with Ratio 2.0 you can get in theory higher topspeeds.
Again a little example. Imagine we have an F1 engine which is capable of a maximum of 18.000 rpm (rpm means revolution per minute).
Ratio 2.0: The motor does 18000 rpm, and the driving wheel 9000 rpm. (higher ratio)
Ratio 9.0: The motor does 18000 rpm, and the driving wheel 2000 rpm. (smaller ratio)
Its obvios that the Ratio 2.0 is in theory able to produce a higher speed when the engine runs 18000 rpm, so its a taller/higher ratio.

Ok now everytime you change your gear you change your gear ratio. So lets make a really fictional example. Assume we built up a F1 car with a 3 gears gearbox. Our F1 engine is capable of a maximum of 18000 rpm.

1st Gear Ratio 9.0 assuming the motor does 18000rpm, the driving wheel does 2000rpm
2nd Gear Ratio 6.0 assuming the motor does 18000rpm, the driving wheel does 3000rpm
3rd Gear Ratio 3.0 assuming the motor does 18000rpm, the driving wheel does 6000rpm
Surely you can see that with 3rd Gear you can make higher Top Speeds than with 1st Gear, its so obvious cause the driving wheel gets more rpm (6000) in 3rd gear with our maximum motor rpm (18000).

In a real car you have a lot of “pinions” (e.g. differential gear) which together (by a multiplication factor) forms a ratio beetween motor rpm and driving wheel rpm. This ratio we will define as the variable “ic”.
So the transmission of any car is considered to be all intermediate gears and systems to get the engine rotational power to the wheels. In reality this comes down to the gearbox and differential, which are both assembled into the gearbox casing.
Additionally you have friction etc. But for our purposes we exclude that information. In general it is absolutely sufficient to think about 2 rotating pinions, one is the motor, the other is our driving wheel, like we do in our example.

Now as we have built up our virtual F1 car with a 3-gear gearbox I will give you some more facts about our fictional engine (facts are based on real f1 engine fact sheets in 2008) :
Redline – Max (limited) rpm: 20.000
Peak Power: 560kw at 19.000rpm
Peak Torque:  320NM at 14.000rpm

The "Motor Torque Characteristics" look something like that. No worries, we come back to that picture later.

But what is Torque?
Ok racers now it gets important. When you have already enough just get a cup of coffee and go on later. With the understanding of torque and more specific a machine (motor) torque we are able to lift the whole idea behind gear boxes.
Lets start slowly and with the basics.
Wiki says: “Torque, moment or moment of force, is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist to an object. Mathematically, torque is defined as the product of force and the lever-arm distance, which tends to produce rotation.”
Now I lift one secret.
The gearing of the drive train must be chosen appropriately to make the most of the motor's torque characteristics.

Before we go deeper into the motor torque characteristics lets learn some important facts about torque. Imagine two pinions. For simplicity lets assume there is no friction etc.
The first is our motor pinion directly linked to the crankshaft.
The second is our differential directly linked to the axes of our driving wheels.
Lets assume the motor does 16.000 rpm with a torque of 305 Nm.
With a gear ratio of 1.0 the torque and rpm at the differential would be the same.
With a gear ratio of 2.0 things change, as the differential pinion does only 8.000 rpm. But what happens with the torque? It doubles! So we have 610Nm torque now on the differential.
So we can’t drive as fast as with gear ratio 2.0 but we have a lot of torque to accelerate now!
By the way there isn’t any energy added cause we got the doubled torque by halve the rpm.
Perhaps you want to check again a video I posted a few days ago for warm up reasons, where this fact is explained.

Now lets have a look at this nice f1 car.

So our heart is the motor with Power P.e and Torque T.m
The motor does n.m rpm.
GB is our Gearbox with the gear ratios. The Gearbox transfers the Engine Torque to the differential and finally the differential transfers torque to the driven wheels with a radius r.k.
The torque realized upon the driven wheels therefore is T.k
Finally through the slip between the tyres and the ground our car moves with a Force F.
Remembering what I told you about gear ratios and Torque. The final Torque realized upon the driven wheels is the product of the initial motor torque and the gear ratio. That product in a formula is:    T.k=T.m*ic

What you can see in the formula is the fact that the higher the ic (Gear ratio) the higher the Torque realized upon the driven wheels. Thats the reason why a car accelerate faster in lets say Gear 1 (e.g. ratio 9.0) than in Gear 2 (e.g. ratio 6.0). But as you also all know the topspeed in Gear 1 is pretty limited, due to the fact that we give away rpm upon the driven wheels. (we raise the torque by factor 9, while reducing the rpm by Factor 9).
So indeed by shortening (small) ratios we have more final Torque realized upon the driven wheels which should result in higher acceleration.

We can extend our formula to:
F=T.k/r.k
F=(T.m*ic)/r.k
F~(T.m*ic) (assuming the radius of the tyres is constant)

So the Force which moves/accelerates our f1 car is proportional to the Product of torque realized upon driven wheels and the gear ratio.

Ok. So lets raise all gear ratios to maximum. In F12011 we would do that by setting all sliders fully to the left side. We would end up with a 7th gear which Topspeed is much to low and we would hit the rev limiter on every single straight.  When we would now just adjust the 7th gear to the needed topspeed we would have a massive drop in Power and Torque by shifting from 6th to 7th gear as the engine would fall in a very low rpm window.
Another important thing is that we haven’t talked about traction yet. So as you can see we have “maximum” Torque in the first 3 gears, but as you all know the tyres can’t get that Torque T.k fully into F cause of traction limitations.
So it would be much more important to get maximum realized torque upon the driven wheels from 4rd gear to 7th gear when the aerodynamics works and the traction limitation aren’t any more a problem.
Ok so we want to realize 2 things.
1)    Maximum realized torque from 4th to 7th gear
2)    No massive drop in Power and Torque during shifting in the higher gears

So lets go on with “motor’s torque characteristics”. The varying torque output over the rpm range of a motor can be measured with a dynamometer, and shown as a torque curve.
So lets come back to our f1 engine torque curve.

On the X-Axis you find the rpm the motor does.
On the left hand Y-Axis you can see the Power in kw the motor does.
On the right hand Y-Axis you can see the Torque in nm the motor does.
When you combine all 3 you can see the Power and Torque a motor produces at a specific rpm.
You can see several characteristic points in the graph.
n.T -> torque peak point
n.P -> power output peak point
n.A -> condition A
n.B -> condition B

Now most people think when the engine operates around n.T we have the maximum torque realized on the driving wheels resulting in maximum force F. Well thats not the case. It has been proven that the engine should work as close at the output peak n.P as possible. We could prove that by mathematics now, but that would be kinf of overblown. But I would like to give you a feeling why this is. Lets have a look at the following picture.

You can see two cars a) and b) which want to reach the top of the hill.
In both cases we would have to put the same energy E=mass*velocity of fall*force(height) in the car to relocate the mass (car) from point 0 (hills base) to point 1 (hills top).
The reason is that in case a) and b) the energy we need is not dependant of the velocity or distance it justs depends on mass(car) and height (hill).
But what we are interested in is what happens when we would let race car a) against car b).
So we are interested in the time t the cars need to reach the top of the hill.
What we are interested in here is the proportion of energy and time.
P=energy/time
No lets make a simple example.
The car weights 1000kg and should reach the hills top in 10 seconds.
Ok so P=1000kg*9.81m/s*50/10=49050W=49,05kw.
Now imagine in case a) the car goes with lower speed and a hill gradient of 45 degrees.
On the other hand in case b) the car goes with higher speed and hill gradient of only 10 degrees but a longer distance.
There is a good chance that in both cases the cars reaches the top of the hill after 10 seconds.
What you can see here is a very elementary thing. If both engines have the same maximum output [kw] it doesn’t really matter if engine a) has more torque than engine b).
Newton says: P=F*velocity
Assuming that velocity is constant we get P~F.
So we conclude Pmax~Fmax.
This has enormous meaning in the technical practice since it shows that operating an engine in the area of output peak is the only way to either attain the driving power peak on the wheels of vehicle (go-kart, motorcycle, buggy, …) while the engine torque has absolutely no importance!
Its obvious that on a race circuit you have a mixture of case a) and b). So concentrate in letting operate the engine in the area of output peak by setting the gearbox is the way to go.
Some of you might argue now that this doesn’t really connects to what we have learned before about torque and the relationship to F.
F=(T.m*ic)/r.k
F~(T.m*ic)
Indeed in the first sight it seems that the Initial Engine Torque T.m is the essential variable for getting maximum driving power F.
BUT, what must be considered is the fact that a transference number ic is contained in relationship. Remember ic is the variable for the gear ratios. A pinion can rotate very fast with low torque like the car in case b) or very slow with high torque like the car in case a). So its the product (T.m*ic) which is important (output power) not the torque only.

Lets go back to our F1 motor torque curve.
Now lets assume we decide to limit the rev band to have a maximum drop from P.max of 30KW. As you can see in the graph our engine should operate between 16.400 rpm and 19.000 rpm in every gear. What we get by doing this is a window around the maximun Power Peak where our engine operates in a maximum average power output. So as soon as we leave that window we should shift a gear higher or lower depending on the rpm/speed of our engine.

So a trivial approach to setup a gearbox for that is shown in the next picture.

You can see that in every gear the speed difference is constant (dif)w=31,67 km/h.
Lets analyse the graphic. So imagine we drive in 1st gear until our rev indicator/limiter shows that we should shift. In Codemasters F12011 game this is the case when the rev lights blink in purple color. Now we shift 2nd gear and as you can see the rpm of the engine drops by 3722 rpm (Point a). Now we are out of the peak point window cause we would need at least 16.400rpm to be in it. But for the moment we only have 15.288rpm. By further stepping onto the throttle we will reach the peak point window again at 16.400rpm and raise the rpm until we reach again the 19.000rpm. Again we shift, this time into 3rd gear.
Thats the classical attitude of setting up a gear box.
Getting the lowest top speed in 1st gear, in that case 130km/h and getting the highest top speed in 7th gear in that case 320 km/h. In between every gear has a constant increment in maximum velocities in that case 31,67 km/h.
We said before that the engine should operate as close as possible at its output peak point, which is clearly not the case here.
So we have to make the rpm drop constant for every gear in order to operate in the maximu power peak window.
Lets do that.

What you can clearly see now is that we set (dif)n to 2650rpm to assure that our motor operates between 16.350 and 19.000 rpm.
With adjusting the gear ratio or in other words the possible top speeds for every gear, you set in which rpm the engine starts to operate in next gear!
Immidiately after shifting into a higher gear, the engine rpm should start in the output peak point window.

So far so good.
We haven’t talked much about traction yet. Its obvious that the immense output power and the final torque realized upon the driving wheels in lower gears results in massive wheelspin. What the driver typically does is not using the full power in lower gears. So that leads to the conclusion that we can afford being out of the maximum power peak window in lower gears for a short moment after shifting is done cause we aren’t able to direct transfer the torque T.k in acceleration force F. That gives us the possibility to set the maximum power peak window even smaller and constant from 4th to 7th gear and to get a massive acceleration when shifting from 3rd in 4th gear by setting the engine in the maximum power peak window. You could see it as giving away something from 1st to 3rd gear and then regaining it back in the higher gears. Lets do that.

You can see that now the points a, b and c are out of the maximum power peak window again, which doesn’t really hurt cause of the traction limitations we have in lower gears.Therefore You can see that from point c to f we are in the power peak window which is now needed cause aerodynamics work for traction and we need full power now from the engine given over the gearbox onto the differential and finally upon the driving wheels. The nice thing is that in this approach we could even make the size of the peak power window smaller so we have a higher peak power average distributed over all higher gears.
 
Lets do that approach now in Codemasters F12011 game.
So one optimal gearbox setting for the Nurbuergring in F12011 coud look something like that.

As you can see we made the same approach as discussed in the graph above. This gearbox gave me 3 tenths in qualy mode and even more in race mode when the car has heavy fuel load. The only thing you should change in race mode is shifting every gear 3 clicks to the left due to the fact that the car is heavier and we haven’t drs the whole lap.

Obviously you have to care also about the track layout which is already worked in that gearbox setting.
I will serve that in my next tutorial.
For now I hope you enjoyed this tutorial and that it helps to make you even faster in simracing.

I know that was really hard stuff and a lot of questions rise up (hopefully).
Feel free to ask under comments or under the G+ Website.
I will try to answer every question and hope that this tutorial can be a starting point to care about your gearbox in future!



Keep racing
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