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Let's say I've got a Cessna C172S with a Lycoming IO-360-L2A engine that produces 180 hp (that's the power output for sure). Let's say I've also got a water pump, that is rated at 1 hp (power input or output?).

Is the Lycoming engine 180 times more powerful than my water pump?

Can they be compared with each other - one's based on electricity, and the other is based on fuel combustion)? Or have I got it all wrong? The Airbus E-Fan has 2x30 kW (2x40hp) electric motors, and it's slow (with respect to the 172S), cruising at only around 86 kn.

1 Horsepower = 745.7 Watts

that means 180 HP = 134244 W (or) 134.244 kW! Did I get that right? Again, is that the power draw or the power it can produce (they are kinda different right)? In order to get the same power, should an equivalent electric motor be rated at around 135 kW ?

Let's say I have another (read experimental) aircraft of just a quarter the weight of the 172S and very similar drag-profile. Does that mean I only need a 45 hp engine to achieve similar performance?

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    $\begingroup$ Horsepower is not a unit of work, any more than a knot is a unit of distance... $\endgroup$ – DJohnM Aug 21 '17 at 19:31
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    $\begingroup$ The radio of input and output is known as efficiency. For gas or turbine engine you can calculate the input power or energy consumption rate with fuel consumption rate and fuel's energy density. But for electric motors the efficiency is almost around 90% so the input power is almost the same as output. $\endgroup$ – user3528438 Aug 21 '17 at 19:51
  • $\begingroup$ Horses don't fly, shouldn't it be called eagle power or something? $\endgroup$ – Devil07 Aug 23 '17 at 13:24
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What is horsepower? It is a measure of the work a horse can do in an hour, invented in the time of the steam engines in order to make sense of what they could do, in a time when all work was done by humans and horses. As usual before the SI, there were many definitions of horsepower. Here is the one from wiki, on what a metric horse could do:

enter image description here

Notice that there is a time element in the picture: if the horse takes all day to raise the weight one metre in height, he is not very powerful.

Nowadays, the unit of power is the Watt, after James Watt who coined the horsepower unit to sell his steam engines. It is defined as the force in Newton, required to move 1 kilogram over one meter in one second:

$$1 W = 1 \frac{N \cdot m}{s} $$

In these units, you can see a force times a velocity, and that is one way of looking at what power is: you need more power to drive faster up a hill. But these are linear entities, and most power is made by rotary engines. Rotary units are torque (N*m) and how fast the engine is spinning (rad/s).

With engines, it makes a difference where power is measured. There are always losses caused by friction and by energy conversion, and the closer you measure at the output shaft of the engine, the higher the reading. This is what vehicle manufacturers rather do: car engine power is measured at the crankshaft, not at the wheels that actually propel you over the roads, because between engine and wheels there are transmission losses.

The question why power is used for engine rating, and not force or torque, is an interesting one. It is force that accelerates us: $ F = m \cdot a$. We can gear the motor force or torque output as required - if the gearing had no losses, power before and after gearing would be the same. So horsepower is useful to compare capabilities of engines, regardless of gearings. However they wil always be maximum capabilities.

enter image description here

With an aircraft, the engine power needs to propel the aircraft via the propeller. The propeller delivers thrust T, and can drive the plane at speed V, maximum speed being where drag equals thrust. Engine power is thrust times airspeed, plus the power required to overcome losses: mechanical losses due to friction, and aerodynamic losses due to propeller efficiency.

Your question on having an aircraft a quarter of the weight and similar size. The thrust is required to overcome aerodynamic drag, both friction drag and induced drag from lift. Friction drag will remain equal, lift induced drag will be 1/4th of the full weight version. You will need more than 45 hp to get the quarter weight aircraft to travel at the same cruise speed.

enter image description here

The picture is from this most informative source: parasitic power stays the same, induced power reduces by a factor 4. Notice that at low speeds induced power is dominant, at high speeds parasitic power is dominant. So with a 45 hp engine you will get off the ground if the weight is reduced by factor 4, but the maximum speed will be way less.

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  • $\begingroup$ So that's why electric airplanes are just a distant star in the universe of aviation... Thanks a ton! Also the link to the "most informative source" helps a lot! $\endgroup$ – ClobberXD Aug 22 '17 at 5:34
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    $\begingroup$ Well the electric motors themselves are quite mature, it is just the electricity source, batteries are heavy. $\endgroup$ – Koyovis Aug 22 '17 at 5:50
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    $\begingroup$ In defence of horses, Mr Watt was a shrewd businessman and he chose a pretty old, knackered horse for the canonical horsepower to make his engines seem a little more wonderful. A horse can easily output 12hp for a short period, and only if you use a not particularly outstanding horse for hard work all day might it average about 1hp over the whole day. $\endgroup$ – Dan Sheppard Aug 22 '17 at 19:56
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I apologise if I'm over simplifying, but a piston engines output can generally be measured at the wheels or crank. As aircraft don't have powered wheels, what we are measuring is purely the power that the engine can deliver at the crank/output shaft where we can directly attach our propeller.

When manufacturers list horsepower they really mean 'maximum horsepower'. This is directly calculated from the torque the engine can deliver at a specific RPM. The engine will deliver different (i.e., less) outputs at different speeds. So you can think of horsepower as the calculation of torque multiplied by RPM. (It's actually then divided by an arbitrary value to make it into 'horses') with the list value being the highest combination of torque x rpm the engine can deliver.

Torque is the measure of actual force the rotation of the engine can deliver. So, because RPM is the multiplier, a very very fast but low torque engine may have more BHP than a slow but torquey engine. Think about the difference between a truck and a light sports car - the truck needs a lot more force to move so a high horsepower sports car engine will be useless if it can't deliver the required torque.

Alone, it also says nothing about efficiency or, for example, the amount of time the components can sustain this. Nor does it define how that power is harnessed - 100hp through to a feathered propeller produces different results to a non-feather propeller for example.

As should be clear, a single horsepower value doesn't tell anywhere near the full story about an engine.

For any non-piston engine, we would need this value at some form of output shaft in order to compare it like for like. You'd need more specific details on the measurement of any particular engine to determine where the measurement was taken.

Finally, even when the comparison is 'fair', because power is a product of torque and RPM we can't say two 100hp engines are equal. We would need to know exactly when in the 'power curve' that this power is delivered. This isn't linear, hence the requirement to dynograph engines.

If, however, you could find two engines which deliver the same power at the same RPM (i.e., they'd be the same on a graph) then the performance should be similar. But then, unfortunately, we have to discuss things like response time where, for example, a jet engine can take a long time to spool up but an electric engine can be near instant.

TL;DR Comparing power plants is really very hard, even with full figures. Comparing based on a single number is vaguely indicative at best.

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In addition to the other answers: for internal combustion engines, the rated power is the maximum amount of power the engine can produce, i.e. with full throttle applied and at the optimum point in its rev range. A more comprehensive way to indicate how much power an engine has, is the power/torque curve like this random example:

Power curve

This shows how output power varies with rpm. The peak in this curve is quoted as the rated power.

For electric motors, on the other hand, the input power is often specified, certainly for the sort of electric motor you have at home. For electric motors, this is an important figure because you have to dimension the power supply accordingly: you won't get far if you connect a 10-kW motor to a penlite battery.

Now, electric motors are very efficient: around 95% of input power is converted to motion of the output shaft. Your water pump will convert 950 W to motion and only 50 W to heat.

Internal combustion engines are far less efficient. A really good petrol engine converts about 30% of the energy in its fuel to motion (diesels can get to 40%). The rest is lost as heat and noise, via the cooling system and the exhaust.

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  • $\begingroup$ Diesels can reach or even exceed 50% efficiency. The ones that do are rather large, though, and power ships rather than aircraft. $\endgroup$ – Brian Drummond Aug 22 '17 at 22:08
  • $\begingroup$ Electric motors will replace engines only after batteries' specific energy come close to a half of that of gasoline. Now even with efficiency as low as 30%, internal combustion engines provide more range just because of incredible stores of energy onboard. Even with 70% wasted there is enough. ( $\endgroup$ – Eugene May 21 '18 at 23:06

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