# Engine Horsepower

on . Posted in Fluid Dynamics

Engine horsepower, abbreviated as EHP, is the estimate of engine horsepower after a quarter mile run using the trap speed.  When you see a specification for engine horsepower, it indicates the engine's ability to do work over time.  For example, if an engine is rated at 200 horsepower, it means that the engine can perform 200 times the amount of work that can be done by one horse in a given amount of time.

Engine horsepower is a unit of power that measures the rate at which work is done.  It is commonly used to quantify the power output of internal combustion engines, particularly those used in automobiles, trucks, and other vehicles.  The term "horsepower" was coined by James Watt, a Scottish engineer, to compare the output of steam engines to the power of horses.  One horsepower is defined as 550 foot-pounds per second or 745.7 watts.  This definition was established to determined that a horse could turn a mill wheel of a certain size at a rate that equaled 550 foot-pounds per second.

## Engine Horsepower formulas

$$\large{ EHP = W \; \left( \frac{ v }{ 234 } \right) ^3 }$$

$$\large{ EHP = \frac{ W }{ \left( \frac{ ET }{ 5.825 } \right) ^3 } }$$     (elapsed time)

$$\large{ EHP = W \; \left( \frac{ s }{ 234 } \right) ^3 }$$     (trap-speed)

$$\large{ EHP = \frac{ \tau \;\; s \;(RPM) }{ 5252 } }$$     (rotating horsepower)

$$\large{ EHP_{change} = W \; \left( \frac{ v_2 }{ 234 } \right) ^3 \;-\; W \; \left( \frac{ v_1 }{ 234 } \right) ^3 }$$     (determine increase in horsepower)

$$\large{ EHP_{change} = \frac{ W }{ \left( \frac{ ET_2 }{ 5.825 } \right) ^3 } \;-\; \frac{ W }{ \left( \frac{ ET_1 }{ 5.825 } \right) ^3 } }$$     (determine increase in horsepower with ET)

Symbol English Metric
$$\large{EHP}$$ = engine horsepower $$\large{\frac{lbf-ft}{sec}}$$ $$\large{\frac{Btu}{s}}$$
$$\large{ET}$$ = elapsed time (time to finish quarter mile) $$\large{sec}$$ $$\large{s}$$
$$\large{ET_1}$$ = initial elapsed time (time to finish quarter mile) $$\large{sec}$$ $$\large{s}$$
$$\large{ET_2}$$ = final elapsed time (time to finish quarter mile) $$\large{sec}$$ $$\large{s}$$
$$\large{s}$$ = speed $$\large{\frac{ft}{sec}}$$   $$\large{\frac{m}{s}}$$
$$\large{ \tau }$$  (Greek symbol tau) = torque $$\large{lbf-ft}$$   $$\large{N-m}$$
$$\large{v}$$ = velocity $$\large{\frac{ft}{sec}}$$   $$\large{\frac{m}{s}}$$
$$\large{v_1}$$ = initial velocity $$\large{\frac{ft}{sec}}$$    $$\large{\frac{m}{s}}$$
$$\large{v_2}$$ = final velocity $$\large{\frac{ft}{sec}}$$  $$\large{\frac{m}{s}}$$ Tags: Engine Horsepower