DiscoverHover CURRICULUM GUIDE #20
THRUST
© 2005 World Hovercraft Organization

Possibly the most novel and exciting aspect of the hovercraft is the vertical lift that allows it to hover. You know how to measure velocity and acceleration, and you’ve learned other concepts such as force; torque; power; work; momentum; and how the engine works. All these concepts, as well as others, come into play when the hovercraft’s engine spins the propeller to move the hovercraft forward. When the propeller spins, it pushes against the air. The air, according to Newton's Third Law of Motion, pushes back against the propeller, and the propeller is attached to the hovercraft. The result is that the hovercraft moves forward. We will now investigate in detail how this happens.

Let’s start with a quick review. When the engine spins, it drives the propeller. Remember that we often use different gear ratios so that the propeller turns with less speed and more torque than the engine. When the propeller spins, it can be explained by Bernoulli's Principle and the Coanda Effect for moving air. The amount of air moved depends on the pitch of the propeller and the speed at which it spins. The amount of thrust it produces depends on the amount of air it moves and how much it speeds up the air. We must also remember that a thrust duct can significantly increase the thrust put out by a propeller or fan, and that the thrust becomes less effective as the hovercraft’s speed increases.

How much thrust will you get on a certain hovercraft? That is a complicated question, so let’s start with some basic principles. When the thruster accelerates air by exerting a force, it changes the momentum of the air. Since momentum is conserved, the air exerts an equal amount of force on the propeller so that the hovercraft’s momentum changes by the same amount. It becomes more complicated when we attempt to determine exactly how much air the propeller moves and how fast it moves the air. In 1821, the French engineer Claude-Louis Navier derived equations that describe how fluids (liquids and gases) move and, in 1845, the Englishman George Gabriel Stokes derived a more refined version. In their full form, these equations, known as the Navier-Stokes Equations, describe essentially every type of flow. Their full form, however, is so complex that in more than 150 years nobody has been able to solve the equations in their entirety. Due to this difficulty, it has become common practice to use numerical approximations. Using the Navier-Stokes Equations to their full extent would require knowledge of fluid mechanics and calculus well beyond the scope of this Curriculum Guide. Fortunately, working approximations of propeller behavior have been developed in order to simplify the process. Even the models used by many propeller makers, and by and institutions like NASA, are very rough. These rough models are rather complicated and involved, so the finer points of propeller design will be left for later study. Still, we can use some rules of thumb to determine how well a propeller will work if the airfoil shape and pitch angle are reasonably designed. Basically, the thrust provided by the propeller depends on the rate at which the propeller moves air, the density of the air, and the difference between the velocity of the air flowing into the propeller and the air flowing out. The mass flow of the air is equal to the density of the air multiplied by the velocity of the air and the area of the disc formed by the propeller. This means that there are two aspects of the hovercraft’s thrust system that significantly affect the thrust — the power of the engine and the diameter of the propeller. Note that the thrust is directly proportional to the power and the area. Since the area is based on the square of the diameter, so is the thrust. Barring losses, if you double the power of the engine then you will double the thrust. However, if you double the size of the propeller, the thrust is increased by a factor of four.

In building small hovercraft, a ducted is often constructed around the propeller, which helps substantially increase the static thrust of the engine by making the fan or propeller more efficient. Another way of thinking about this is that the duct has the same effect as increasing the fan or propeller diameter. The duct serves to increase the stream of air moving through the propeller. Other advantages deal with phenomena that occur at the tips of the propeller blades. In an open propeller, the incoming air comes from everywhere, including air from behind the propeller, but outside the stream of exiting air (called the slipstream). This air must move forward, then very quickly turn almost completely around, which causes turbulence at the blade tip. A duct prevents this from happening. Propeller tip vortices in the air are another effect that occurs at the tip of an open propeller. The pressure in front of each blade is lower than the pressure behind the blade, so the air tries to move from the back to the front of the blade, creating a tip vortex. Constructing a duct close to the ends of the propeller blades helps to prevent the formation of pressure tip vortices.

Approximations based on the conservation of momentum have been developed to describe the static thrust of a hovercraft for both a ducted and non-ducted propeller under particularly ideal conditions. Generally, the actual thrust will be 60% to 90% of these approximations. Also, enlarging the diameter of the propeller will increase thrust to a greater degree than will an increase in engine power. The following equations give the force in units of pounds as a function of power (P) and diameter (D).

Open propeller: F_static = 86.79 × (P D)^2/3
Ducted propeller: F_static = 86.79 × (√2 × P D)^2/3

The 86.79 value gives the thrust in Newtons when the power is in kilowatts and the diameter is in meters. Converted to American Customary units, the number is 7.27 to give thrust in pounds, power in horsepower and diameter in feet.

It is usually quite difficult to determine the actual horsepower available at the propeller. We can begin with the engine manufacturer’s power curve, but many times these are overrated. Always try to get the Industrial Rating, which tends to be more accurate. Assume the engine actually produces 90% of the advertised power. A 12.5 hp engine will actually produce only 11.25 hp.

When the hovercraft starts moving, the static thrust becomes less of a factor. The equations for the propeller change and become more complicated. For our convenience, we will describe the thrust in terms of the air flow rate and change in the air velocities. The thrust of a propeller (or even a jet or rocket engine) at speed can be calculated from the relation described earlier, which was:

F = (MFR × v)_exiting − (MFR × v)_entering

Note that the speed of the incoming air comes from the wind velocity in the area and from the velocity of the hovercraft. This is one reason the hovercraft propeller or fan produces less thrust as it travels faster.

In a ducted hovercraft, the static thrust is increased compared to a propeller of the same diameter, but when the hovercraft starts moving quickly the wind resistance against the duct becomes a significant factor. The designer of a speed record-setting hovercraft would calculate the duct resistance and might decide to use a non-ducted propeller. Ducts help at low speed where a large amount of thrust is needed to get over the hump, so it is usually a good idea to use thrust ducts on hovercraft from an aerodynamic standpoint, as long as they are well designed and constructed. A thrust duct also provides a practical means for guarding the propeller or fan.