# Is the effect of weight-to-horsepower ratio linear?

I am wondering if a car that weighs 2,5kg and a engine power output of 1hp would be just as fast when going in a straight line like a 1250kg car with 500hp (they both would have a weight-to-horsepower ratio of 2,5:1). To make things easier, lets ignore things like efficiency, traction and aerodynamics. Are there other factors I am not aware of?

If we ignore friction and drag we can revert back to,

One horsepower is equal to 745.7 watts. one watt is 1kg force moving 1-meter per second.

a car with N times power is being pushed by N times force, and assuming it has n times mass

$$F=m\alpha \quad and\ NF=Nm\alpha$$

The answer is yes, the two cars will accelerate with same acceleration.

Acceleration is determined by power-to-weight ratio. Two vehicles with the same power-to-weight ratio will accelerate at the same rate.

Note however that top speed in level motion does not depend on weight, it depends on another ratio: power-to-drag. Two vehicles with the same power-to-drag ratio will achieve the same top speed- but the heavier one will take more time to get there.

That is why the power to weight ratio is so important.

As seen on Top Gear, one of the quickest cars around the track is/was the Ariel Atom, as it had a mass of less than 1000kg but relatively lots of power.

Other cars had two or three times the horses but the mass crippled them.

Linear up to a point as other factors come into play - gear ratios and power delivery as well as drag. Tire adhesion also becomes a factor. Then tire flexing etc

• But that is exactly my question. The weight-to-horsepower ratio in both cars is the same in my question. And my question excludes factors like drag, aerodynamics, gear ratio etc. May 17, 2022 at 12:35
• you didn't answer the question May 17, 2022 at 13:22