units check for horsepower to weight (Hp/W)

Question

is this units breakdown correct:

Hp/W= (ftlb/s) / (lbft/s^-2) = s^-1?

I think I might made mistake?

Answer 1

You are confused by the units ($lb_m$ - a unit of mass; $lb_f$ - a unit of force). As a matter of force, the units for horsepower is $\dfrac{ft-lb_f}{s}$, and the units for weight (m*g) is $lb_f$. So the resulting units is $ft/s$. This article may clear your confusion. https://en.wikipedia.org/wiki/Pound_(force)#:~:text=The%20international%20standard%20symbol%20for%20the%20pound%20as,mass%20exerts%20one%20pound%20force%20due%20to%20gravity.

ADD:

Hp/W = (ftlb/s) / (lbft/s^-2) = $\dfrac{ft-lb_f}{s}$/$\dfrac{lb_m ft}{s^2}$ = $\dfrac{ft-lb_f}{s}/lb_f$

Note: $\dfrac{lb_m ft}{s^2}$ = $lb_m*\dfrac{ft}{s^2}$ = $m*a$ = $F$, or = $m*g$ = $W$

Answer 2

Horsepower over weight is fundamentally Power over Force. Since, a common formula connecting Power and force is:

$$ P = F\cdot v$$

where

• P is the Power
• F is force
• v is velocity

you can obtain from the above, that the units of $P\over F $ are equal to the units of velocity i.e. Units of length over time