# Are these units correct for Hp/W

using the table provided, and how it says the Velocity should be in mph, is it correct to say that the units of hp/W only taken from this table, using the formula from the table is mph also?

Horsepower is a measure of the amount of work done over a period of time. Specifically, one horsepower is the amount of effort required to lift 33,000 pounds one foot in one minute. Note the basic unit for velocity is $$ft/s$$ (length/time), which can be expressed as "$$ft/min$$" and "$$mph$$" through unit conversion.

$$\dfrac{ft}{s} = \dfrac{ft}{s} (\dfrac{60s}{1min}) = 60\dfrac{ft}{min}$$, and

$$\dfrac{ft}{min} = \dfrac{ft}{min} (\dfrac{1mi}{5280ft}) (\dfrac{60min}{1hr}) \approx 0.0114 mph$$

• Hi, sorry I’m confused, so from the table, as it uses V is in mph, am I right? Mar 29, 2022 at 18:29
• Nothing wrong with the table. As pointed out in your previous post, Hp/W = V (velocity), which (the velocity) can have the unit "ft/s", "ft/min", or "mi/hr" (mph) since they all have the form of (length/time).
– r13
Mar 29, 2022 at 18:53
• So in this case, is the units of hp/W mph please if I input V in mph? Mar 29, 2022 at 19:22
• Yes, input V in mph only if you use the given equation (hp/Wo = a*V^C) with the constants (a, C) in the table. The unit conversion should have already been taken care of during the development of the constants.
– r13
Mar 29, 2022 at 21:24
• For example, let's solve the engine power required for the "flying boat" case. For which, a = 0.029, C = 0.23. Assume the boat weigh Wo = 1000 lbs, and driving speed V = 50 mph, then Engine Power = 1000*(0.029)*(50^0.23) = 71.3 hp. Note, the calculation is not valid for cases not covered by the table.
– r13
Mar 29, 2022 at 22:28