Mach Number, World Records, and Propellers

Mach number has been tossed around so often in the popular press since the 1950's that the word has seeped in to the public argot. Cars and soap powders are named "Mach 1", or maybe "Mach 2" when they become "new and improved". Mach number is an important parameter in many `full size' aircraft design and operations. For scale models the importance for aircraft design is essentially nil, but there is still a possible problem with propellers at the model scale.

The Mach number, named after the Austrian scientist Ernst Mach (1836-1916), is the ratio of a velocity of an object in a fluid medium to the speed of sound in the medium. "Speed of sound" means the velocity with which very small pressure disturbances travel. For air over the whole range of pressures and temperatures that aircraft operate in this speed depends only on the temperature. In air at normal conditions it is in the range of 600 to 700 mph. (Statute miles per hour). In water, for example, the speed of sound is many times larger than it is in air.

At Mach numbers beyond 0.7 or so the fact that the air is compressible has an increasing influence on the flow around a body. At Mach number 1 and above the flow is radically different. For this reason the words "compressibility effects" and Mach number are synonymous. The Mach number at which compressibility effects become large and drag begins to rise very rapidly is called the "drag divergence" Mach number.

Propeller tips can get close to or past the airfoil critical Mach number. The compressibility effects include a rapid increase in drag and shock stalls. This note will explain how to test for this kind of problem in your model. It may NOT be a problem if you want a lot of prop noise. In that case you'll find out how to makes sure you create the noise you love.

The graph below shows the speed of sound for air as a function of temperature. The graph is in "model builder units", that is speed in US statute miles per hour and temperature in degrees F.

Remember the F-86? Even with the swept back wing the critical Mach number was a problem. With that airplane, as with most of them in that era, the critical Mach number fixed the maximum speed. Despite adding more power the level flight top speed increased very little, staying close to the critical Mach number.

The British had captured the aircraft speed record after the war. The rules were that the flight would take place at an altitude of about 75 meters and the aircraft was not allowed to exceed something like 300 meters during the whole flight. Further, once a record was set, it had to be exceeded by 3% in order to break it.

The US Air Force and North American recognized the F86 had the potential to break the record. They wanted to capture the record for the U.S., but they wanted to put it out of reach for a significant length of time.

So if you are stuck at a given Mach number you go faster where it's hot, and the U.S. had hot places.

On July 16, 1954 the F86-D set a world speed record of 715.7 mph at Salton Sea, CA. Summer in the California Desert at sea level. Look at the graph below. You'll see that going from 60 F to 100 F is worth more than 3.5% in speed at 0.9 Mach number.

So why is the "critical Mach number" less than 1 and when do propeller blades run up against it?

The airflow over a lifting airfoil is accelerated. The speeds at some point on the airfoil will be significantly higher than the velocity of the airfoil relative to the air. So local supersonic flow is possible at subsonic speeds,and drag rise begins near this speed. Thick airfoils and airfoils at high angle of attack have a lower drag divergence Mach number and at the low Reynolds numbers model propellers run at the divergence Mach number can be as low as 0.6. As a rule any Mach number over 0.7 will be experiencing some transonic drag rise if it operates with any lift.

As a check the graph below will give you some idea about the propeller tip Mach number and whether it is high enough to give you any problem. See the next graph for an example of drag divergence.

Drag divergence Mach number from some tunnel tests on relatively small chord airfoils is shown in the last graph. The data are for a NACA 4-digit airfoil similar to that used on model aircraft propellers, although not the best choice! There are curves for 12% and 6% thick sections and several angles of attack. Note that for the 12% section drag divergence can begin at very low mach numbers.