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is this units breakdown correct:

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

I think I might made mistake?

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  • $\begingroup$ 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. $\endgroup$
    – Tiger Guy
    Commented Mar 29, 2022 at 15:35
  • $\begingroup$ By W you do mean Watts don't you? $\endgroup$
    – Solar Mike
    Commented Mar 29, 2022 at 15:50

2 Answers 2

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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 = $m*g$ = $W$

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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

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