Many of our club members, and others in the aviation community, have been increasing the horsepower of their aircraft, in the search for speed. I thought it might be useful to take a look at this popular mod from a technical point of view.

When we look for more speed by increasing horsepower, we are up against what is called the "cube law". When an airplane goes faster, three components of the thrust Vs drag equation change. The first, and dominant component is form drag. Form drag is the drag created by the size and shape of the aircraft, and the amount of air that must be moved aside for the aircraft to move through the air. Form drag is often called "parasitic drag" because it does no good at all. Form drag increases in proportion to the cube of the airspeed. Another component is the induced drag. This is the drag resulting from the lift that is created by the wings. Induced drag decreases in direct proportion to airspeed. The final component is thrust. The efficiency of a propeller in converting horsepower to thrust is reduced as airspeed increases.

The total of these influences results in the so called cube law. That is, to increase speed, power must be increased by the cube of the speed increase. So, to double the airspeed, power must be increased by a factor of eight. The other direction of the equation is, if you double the power, the speed is increased by the cube root of two, or 1.26 (26%). If we stuffed 600 horsepower in a 185 that used to cruise at 147 kts on 300 Hp, the new cruise speed would be 1.26 times 147 equals 185 kts.

A popular mod in our club has been to replace the O-470 in a 180 with some version of an O-520. I did this at Texas Skyways. They claim the carburated 520 produces 280 horsepower at 2700 rpm. This is 5 horsepower less than the fuel injected version. Looking up the horsepower vs speed tables in the owner’s manual, the stock 180K cruises at 142 kts at 8000 feet, at 74% power. The O-470U is producing 170 hp. At the same altitude, and the same 2400 rpm, the O-520 is producing 180 hp. To calculate the resulting speed increase, we divide 180 by 170 equals 1.0588, then take the cube root equals 1.0192. Multiply the old book speed of 142 kts times 1.0192 equals the new cruise speed of 144.7 kts. This is almost exactly what I saw on my airplane.

The other performance increase we see with increased horsepower is increased rate of climb. This too, can be calculated. One horsepower equals 550 ft-lb per second, or 33,000 ft-lb per minute. This means that one horsepower can lift 550 lbs one foot in one second, or 110 lbs five feet in one second, etc. In an aircraft at climb airspeed, a certain amount of horsepower (thrust) is being used to keep the aircraft flying. Any additional horsepower that is available results in a climb. We can work backward to find the horsepower required for level flight at climb speed by subtracting the power required to climb. For my 180, at 2800 lbs, the book says the rate of climb at sea level is 1080 ft per minute. Assuming a prop efficiency of 75%, 1080 times 2800 equals 3,024,000, divided by 33,000 equals 91.6, divided by .75 equals 122 horsepower being used to climb. This implies that 108 horsepower is being used to maintain level flight at climb speed. If we swap for a 280 hp engine, we should have 172 hp available for climb. (This assumes there was no weight change with the engine swap.) This should give a new climb rate of 172 times .75 times 33,000, divided by 2800 equals 1521 ft per minute climb (a 440 ft per minute increase). If you also include the gross weight increase kit I installed, 172 times .75 times 33,000 divided by 3190 equals 1335 ft per minute. Still better than stock by 255 ft per min.

You can see from the above calculations that a horsepower increase will increase rate of climb more than speed. When you also consider the increase in fuel consumption, the pursuit of speed via horsepower doesn’t make any sense to a cheapskate like me. Horsepower will increase the load carrying capacity, and safety via improved climbing ability. If you want to go fast, work on reducing form drag. A 5% reduction in drag will result in a 5% increase in speed, with no increase in fuel consumption.

Fly safe and have fun.

John Huft