[To understand the material of these documents, I assume the reader have a firm understanding of Newtonian Kinematics.]
I learned how to drive in an automatic car when I was in Michigan. But when it came to buying a car last year, I didn't care too much about whether it was manual or automatic. I reckoned that if it was a manual one, I could find someone to teach me and I simply learned one more skill.
Maybe it was fate, I picked up a red '93 Mazda Protege DX. It is a manual car. I didn't know what's so special about manual cars. I used to think that the technology is advanced enough that the user-friendliness of automatic is achieved without any sacrifice of performance. It turns out I was wrong. [Well, in the case of the F1 gear box in Ferrari 360 Modena F1 or the still lab-testing Continuous Variable Transmission (CVT), it is the other case. Unfortunately, these transmissions are neither reasonably priced nor real.] After learning all the nuts and bolts of car physics, I am glad that I picked a manual car.
In a manual car, in addition to the steering wheel, the other thing you can control is the gear. My manual car teachers (my ex-roommate and a friend) taught me to shift up a gear when I feel that the engine is kind of noisy at the current gear. Based on this criteria, something like 3000 rpm is their recommended shift point. I didn't doubt about it back then. I just followed what they said and shifted the gears like that for a year until I understand all the fuss of car physics. Now I can drive to max out the performance of my car whenever I want it. for those of you driving automatic Camries who feel uneasy when you are beaten by my lowly Protege, I hope all these discussions can serve as an inspiration for you to learn manual or make the bucks to get a 360 Modena F1! (n_n)
I will start the discussion with the effect gearing brought to the conversion between the readings on speedometer and tachometer. Next, I will look at how gearing impact the Net Force formula I stated earlier. And finally, I will round out the discussion with a short conclusion about gearing's effect on maximum speed and acceleration. I will extend the gearing discussion in the Optimal Shift Point section. That section will also contains recommendations for transmission/gear box modifications.
When I was learning how to drive, I was taught to take a glance at the speedometer once a while to see how fast my car is going. I keep doing this over and over but there is always one thing that bothers me - the meter with 123... with an area in red at the end. I was at first puzzled by it. I was thinking the front panel of a car is the most important space in the car. It should only house the equipment that displays the most important instantaneous information. It turns out my guess is right. That meter is used to measure the engine speed. It is called tachometer.
My further research reveals that the readings of speedometer and tachometer are directly proportional to each other. There is a conversion formula to convert engine speed to speed of the car:
| v | = | velocity of the car (ms-1) |
| r | = | radius of tire (m) |
| ω | = | engine speed in rotations per second (s-1) |
| G | = | final drive ratio (no unit) |
| gk | = | k-th gear ratio (no unit) |
Now it is time to use our Skyline to illustrate this formula. Our Skyline has G = 3.545, r = 0.3266m.
| Gear | 1st | 2nd | 3rd | 4th | 5th | 6th | reverse |
| Gear Ratio | 3.827 | 2.36 | 1.685 | 1.312 | 1 | 0.793 | 3.28 |
| Velocity/1000rpm (km/h) | 9.08 | 14.72 | 20.61 | 26.47 | 34.73 | 43.8 | 10.59 |
| Top Speed (km/h) | 77.14 | 125.09 | 175.21 | 225.02 | 295.22 | 372.29 | 90.01 |
Note that the faster your engine motor is rotating, the louder the engine gets. So the more familiar you are with your car's engine sound at different engine speeds, the less you need to look at the tachometer. Professional racers usually don't read the speedometer or the tachometer. This is because given the gear ratios and the engine sound, they can determine roughly the speed of their cars.
From the formula and the table we derived, we can see that the higher the gear ratio (ie the lower gear), the lower the maximum speed you can attain at that gear given the engine red line. That means higher gear (lower gear ratio) gives you higher maximum speed. It also shows that if you want to increase the maximum speed for every gear, you can decrease your final drive ratio.
Increasing your maximum speed is certainly a good thing. So a question you probably will ask is: why don't people simply make a transmission with a very small final drive ratio? To keep you reading, let me leave the answer to the next section.
Recall our net force formula:
| Γ(ω)Ggk | 1 | |||||||
| F | = | ------------ | − | crrmg | − | -- | cdAρv2, | where |
| r | 2 |
We know that the higher final drive ratio G or gear ratio gk, the more force exerted by the engine; hence more acceleration. This leads to an obvious conclusion: lower gear (higher gear ratio) gives you higher acceleration; higher final drive ratio gives higher acceleration in every gear.
So there is a trade-off between maximum speed and acceleration when we are talking about gearing. If you double the gear ratio, you doubled the acceleration but you also halved the maximum speed. That's a pretty tough trade-off. You can have the best of both world only if you raise the engine red line or the torque curve. In the Optimal Shift Point section, in addition to gear shifting tips, I will also provide some simple guidelines to tune the gearing such that you can fully utilize the extra power you gained from other modifications. Keep Reading! ^_^