# units check for horsepower to weight (Hp/W)

is this units breakdown correct:

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

I think I might made mistake?

• using horsepower, the units will be HP/pound or hp/ton most likely. Hp has a conversion factor in it, 33000 ft-lb/min/HP. Commented Mar 29, 2022 at 15:35
• By W you do mean Watts don't you? Commented Mar 29, 2022 at 15:50

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.

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 = $$m*g$$ = $$W$$

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