nowadays there is so much to prepare a gearbox, but none compares to this tuning real
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Hello Guys, today Ill show you how to setup the gearbox relations for each gear.
Lets start establishing some hypothesis, the engines curve, top speed and climb ability.
Lets suppose that:
The car uses 205/60 15 tires, it will give us 0.304m as dynamic radius;
2.11m of frontal area and a drag coefficient of 0.31;
The cars weight is 1250 kg (something like a Honda Civic);
Cars max torque is 190Nm @4600rpm;
The car needs to climb a 60% ramp with 320 kg more than his normal weight (load);
We have an important relation between torque (in Nm) and power (in KW): (Where T is engines torque and N is engine rpm)
Before start to set cars gears we need to know the forces involved in displacement process, I will talk a little bit about each one of them:
1) Rolling resistance force: Like the name says, its a reaction force between tire and ground. Its a product between a rolling resistance coefficient (that depends on tire and ground) and the normal force in wheel. Its a simple equation:
2) Aerodynamic resistance: In lower speeds its totally inexpressive, but is fundamental to determine cars top speed. Its the product between airs density, cars frontal area, drag coefficient and the square of cars speed.
3) Inertia: In higher speeds its inexpressive too (for this analysis), but so significant when the car needs to start a movement. Its the product between rotational inertia coefficient, vehicles mass and acceleration.
4) Slope: the most known force, product between mass, gravity and angles sine (sen).
Now we know this forces and the relation between power and torque, lets check the engines torque (red) and power (blue) curve:
Now we can start to calculate the gears, beginning with the 5th, I would like my car can reach at least 210km/h and Ill suppose the car get this speed in engines max power point, we call it optimum project. We can setup this speed to occur before or after this point, it will give us more top speed or more acceleration.
The equation is so simple, we sum the aerodynamic resistance and rolling resistance and call it resistant torque, this value must to be equal engines torque multiplied by gear and differential relation:
Resistant Torque = Engines Torque (@6000rpm) x (5th gear x differential)
Lets choose the 5th gear relation 0.7:1, so the unique variable we dont know is the differential, if we see the parenthesis like just one thing we will find a value for relation and dividing it by 0.7 we have the differential. For this case its 4.58:1.
The top speed formula (in m/s) is: (raioDinamico = Dynamic radius, N = rpm),and for this case its 215km/h. Next problem now its to set 1st gear, defined by our ramp maximum inclination.
Our resistant torque now is rolling resistance plus inertia and slope, in engines maximum torque (4650rpm). Solving this relation we have 2.82:1 for first gear.
Now we have first and last gear defined, lets find the 3 remaining gears. This is the easiest part, there are basically two ways to get it, first one it geometrical method, it consists to setup an equal gap between the gears and its used to set up trucks gearboxes relations because of the high number of gears they have. For passenger cars we use progressive method, it gives more acceleration in first gears and more speed in last ones. In progressive method we setup the gears like this: n(i)= [n(i+1)*(2*n(i-1)-n(i))]/n(i-1)
My relations for this gearbox were:
Now we have all gearbox defined and its possible to look at some interesting graphics, first of all we have a comparison between resistant torque in each gear and engines torque curve (in red). Notice that last curve touches engines torque curve at 6000rpm, setting our maximum speed, exactly like we wanted to.
We can see the speed map too, that shows the relation between vehicles speed in actual gear and the engines RPM:
We could also calculate trative force and show vehicle performance map, but its for another post. Thats all for today, if any of you want to see the calculation I did, I can provide you a maple file with it, or the same thing in pdf for who dont have this software.
Thanks for reading,
Rafael Basilio
💡 I remember that thread. Reading the first line gave me a good laugh and a few other peoples posts too.
