If you want to limit the discussion to recip piston engines, consider these two cases:
First we have an engine with a flat "torque" curve over its rpm range. This engine would also have a power curve that increases linearly with engine rpm.
Second we have an engine that has a peak "torque" hump in the middle of its rpm range equivalent to the torque of the first engine. This engine would have a power curve that has a peak power equivalent to the first engine only at one engine speed.
If the first engine is used in a car with a one-speed transmission, and the second engine is used in a car equipped with a transmission that has an infinite number of gears, which car would be faster around a road course?
The answer depends on the road course, on the exact meaning of the “infinite number of gears”, on the rev limit of the first engine.
Provided you mean that:
1. The rev limit of the first engine is higher than the revs of the peak torque of the 2nd engine (which means the 1st engine peak power is higher then the peak power of the 2nd engine),
2. The transmission of the 2nd car has not just “infinite number of gears” (which could mean transmission ratios anywhere between 3.1:1 and 3.2:1) but an unlimited range of continuously variable transmission ratios (like, say, from 1000000:1 to 0.000001:1),
then the answer depends on the road course and on the single transmission ratio of the 1st car.
If the “road course” is slow enough (say it does not allow speeds over 150 Km/h) or short enough (say 400m from the start to the end), the 2nd car can be faster because from the beginning of the motion to the end of the motion all the peak power of the 2nd car is used to move the car. In comparison, at low speeds only a small percentage of the peak power of the 1st car can be used for its motion.
If the “road course” is fast enough and long enough, the 1st car can be the winner.
For instance, if the 1st engine has a peak power of 200 bhp at 10000 rpm, corresponding to, say, a speed of 200 Km/h (with its single gear ratio), while the 2nd car has a peak power of only 150 bhp at 7500 rpm, then:
At 50 Km the 1st car has only 50 bhp to accelerate it, while the 2nd car accelerates with all the 150 bhp of its engine.
At 100 Km/h the 1st car has only 100 bhp to move it, while the 2nd car has 150 bhp.
At 150 Km/h the 1st car and the 2nd car have both 150 bhp to push them forwards.
At 200 Km/h the 1st car has 200 bhp to push it forwards, while the 2nd car has only 150 bhp.
If the two cars move at speeds permanently above 150 Km/h, the 1st is faster.
If the two cars move at speeds lower than 150 Km/h, the 2nd is faster.
Way more interesting is the problem of the optimization of the gear-box ratios, especially for engines with peaky torque curve like the old 2-strokes:
Take a look at http://www.pattakon....attakonEduc.htm
, at the RoadLoad DOS program (near the bottom of the page).