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In a book "How a car works" I have read such sentence:

The crown wheel usually has about four times as many teeth as the pinion gear, causing the wheels to turn at a quarter the propeller-shaft speed

Does this mean that if crown wheel had the same amount of teeth then cars would ride 4 x times faster?

4 Answers 4

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In theory yes but in practice no because if crown wheel and pinion had the same number of teeth, differential (axle, final drive) ratio would be 1:1 and the total torque multiplication (transmission gear ratio*Final drive ratio) would not be high enough to propel the car forward. In addition to this, there are far more limitations for a car to ride 4x faster like aerodynamics, tire speed range, stability, engine power, etc.

A simple example: Imagine a car has 3.455:1 1st gear ratio, 0.795:1 5th (top gear) ratio and 4.529:1 Differential ratio. The overall torque multiplication in 1st gear is 15.647 (3.455x4.529), 3.600 in 5th gear (0.795x4.529). Now imagine the same car had 1:1 final drive ratio (same number of crown wheel and pinion teeth). Then overall torque multiplication in 1st gear would be 3.455 (3.455x1) What do the above numbers mean? 3.455 < 3.600

It means that with 1:1 final drive ratio, your car has even less wheel torque than the 5th gear with 4.529 differential! Your 1st gear would be even weaker than your 5th gear! Your car wouldn't even have enough power to move!

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TL DR: Mathematically, it makes sense, but basically it won't work that way.

If there were the same number of teeth, the axle/wheel rotational speed would be the same. This is simple math ... 1:1 ratio. However, one of the reasons we don't do this is for mechanical advantage.

The two gears we are talking about here are typically called the ring and pinion gears. The mechanical advantage they provide is to multiply the torque output coming from the driveshaft (which comes from the transmission, and before that the engine). It does this by allowing the driveshaft to turn (in your approximation) four turns before the axle turns once. This is a 4:1 torque multiplication, which gives the car a great advantage in getting rolling. To overcome this difference if it were 1:1, you'd need four times as much torque, which isn't a good thing, especially when we can get the job done for less.

You stated it "has approximately four times as many teeth". This truly is an approximation, because in actuality, differential gear ratios in passenger cars usually run ~2.75:1 to ~3.50:1 which depends on how the manufacturer wants it setup to balance the final drive ratio at the need of the vehicle. Performance enthusiasts will run their gearing in the 4:1 range or even higher. You will find those who are going for top speed will be running much lower. NOTE: When I say "higher", I mean numerically higher. 5:1 is numerically higher than 3:1.

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The maximum car speed is due to the engine power being used to counter or overcome two friction forces: aerodynamic and rotational.

After about 40mph the aerodynamic forces are larger.

This is why car body shapes are designed to be slippery or aerodynamic.

So not only do you change the gearing but the power as well, however the aerodynamic forces increase with the cube of the velocity so the faster you go the more engine power you need. Otherwise stated as your speed increases the more air you have to move out of the way.

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If it were only that easy! My last truck was a Dodge Ram 1500 with the Hemi. Decently powerful. Except it was made with a 3.55:1 axle ratio, which is pretty high for a truck. I went up on my tires from a 265/70 R 17 to a 285/70 R17. The new tires weren't much taller, but I sure felt the immediate drop of power.

My current truck is a Dodge Ram 2500 with a Cummins and it has a 3.73:1 rear end, and again taller tires. I can't tell I've lost any power with these, but I've gone from around 400 lb/ft of torque to somewhere around 800 lb/ft.

It takes a lot of added power to be able to go up much in gearing. Additionally the stresses on the entire drivetrain increase with higher gearing. If you ever want to run some calculations that will really help on this subject, calculate the total gearing of a vehicle in 1st gear. Most vehicles have the final gear as a 1:1, and maybe an overdrive. The Allison 1000 transmission has 2 overdrives from 2006 on because the diesel engines have the additional torque to drive a 0.614:1 gearing on the interstate. 1st gear is 3.094:1 for comparison.

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