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Designer's Notebook

January 2012 Issue

Wind Tunnel

The STOL equation.

Creating an airplane that can take off or land almost anywhere has intrigued designers since the very early days of flight. True STOL (short takeoff and landing) capability can make an airplane nearly independent of airports. A STOL airplane must be able to both take off and land in a very short distance, as it's not particularly useful to be able to take off from a runway you can't land on in the first place. Even worse is an airplane that can land short, but lacks the takeoff performance to safely depart the same field.

The length of the takeoff roll is proportional to the liftoff speed squared. A relatively small reduction in liftoff speed can significantly reduce ground roll.

Short Takeoff

A takeoff consists of two segments: the ground roll and the initial climb over an obstacle.

Ground roll: During the ground roll, the airplane must accelerate from a complete stop to liftoff speed. The length of the roll depends on two factors: liftoff speed and the acceleration the airplane can achieve. To minimize the length of the takeoff roll we must maximize acceleration and minimize liftoff speed.

Acceleration: The distance required to get to liftoff speed is inversely proportional to the acceleration the airplane can achieve. Double the acceleration, and you halve the takeoff roll. Acceleration is determined by the mass of the airplane and the excess thrust available, which is the amount of thrust available over and above that required to overcome aerodynamic drag and rolling friction. Lots of power helps. A high power-to-weight ratio is one key to short takeoff.

The prop is the other piece of the equation. The prop converts the shaft horsepower of the engine to thrust. For a given horsepower, a large-diameter, low-pitch prop will generate more thrust at low airspeed than a smaller diameter prop with higher pitch. A good example of the high-diameter, low-pitch approach is the combination of prop speed reduction units and props used on modern ultralights. Ultralights also show us why it's not so simple for airplanes that have to go anywhere after takeoff. Having a fixed-pitch prop optimized for low-speed acceleration is like being stuck in first gear. The initial acceleration is great, but the prop will severely limit top speed. In cruise, the airplane needs a prop with more pitch to absorb the power of the engine at the higher airspeed without over-revving.

If the cruise performance of a pure takeoff-optimized fixed-pitch prop is unacceptable, the designer has two choices. The first is to use a compromise fixed-pitch prop that has more pitch than is optimum for takeoff and try to get an acceptable balance between takeoff acceleration and cruise. The second option is to make the inevitable "money for performance" trade and use a variable-pitch or constant-speed propeller.

Liftoff speed: The takeoff roll is proportional to liftoff speed squared. Double the liftoff speed, and you quadruple takeoff roll. Cut liftoff speed in half, and you cut one quarter of the distance. To get an idea of how powerful this squared function is, consider an airplane that lifts off at 60 knots, and has a 1000-foot takeoff roll. Reducing liftoff speed to 50 knots reduces the takeoff roll to 695 feet. If liftoff speed were 40 knots, the roll would be 444 feet, or less than half of that required to get to 60.

This speed-squared effect is the reason that ultralights, and similar very low wing loading planes can take off in such short distances. Even though the acceleration generated by their propulsion system may be unremarkable, they don't have to get going very fast to take off.

To fly away safely, the plane must have a reasonable margin above stall speed at liftoff. Minimum liftoff speed is determined by stall speed, which is a function of the wing loading of the airplane and the maximum lift coefficient of the wing.

Low wing loading is the simple way to minimize stall and liftoff speed. Early airplanes were all STOL. They had to be because there were no airports. Airfields were small grassy fields with no defined runways. The fighter designers of the time tended to prize maneuverability over speed. Early airliners followed essentially the same design philosophy. The British Handley Page H.P.42 Hannibal and the American Curtiss Condor biplane airliners both were capable of very short takeoff and landing, but were so slow that it was almost faster to take a train. Modern ultralights are another example of the "lots of wing" approach to STOL.

Low wing loading keeps stall speeds down but also keeps cruise performance low and hurts ride quality in turbulence. To increase wing loading to improve up-and-away performance, we must increase the maximum lift coefficient of the wing. This is the job of the high lift system. Using effective flaps and, if necessary, leading-edge slats or other devices, the designer can greatly increase the maximum lift available from each square foot of wing. This reduces stall speed or allows the wing loading to increase at constant stall speed. The higher the wing loading, the more sophisticated a high lift system will be required.

Climb: The critical distance for a takeoff is the total distance from the starting point required to lift off and clear an obstacle. For a STOL airplane, a safely positive rate of climb is not enough. Small landing sites are often surrounded by large trees. The need to clear obstacles means that climb angle is more important than climb rate for the first 50 to 100 feet of climb. The goal is not to gain altitude in minimum time, but in minimum distance traveled over the ground.

The majority of a plane's drag at liftoff speeds is induced drag. Induced drag is inversely proportional to airspeed squared, so slowing an airplane dramatically increases drag. A 10% reduction in airspeed increases induced drag 20%. This is even more important for STOL airplanes. If an effective high lift system allows a low-speed liftoff, the airplane will be on the back side of the power curve when it breaks ground. The induced drag will be high, and the airplane will need a lot of power to climb away successfully.

The climb power problem is acute if the airplane has a relatively small wing and is depending on powerful flaps and possibly leading-edge devices to get high lift. Powerful flaps are effective at increasing maximum lift, but they also generate parasite drag. The smaller wing means that the airplane will have a higher span loading, which increases induced drag. Increasing aspect ratio to keep the span loading down with a smaller wing area can help alleviate this problem, but at the cost of increased wing weight.

Once again, the designer faces a compromise. A low wing loading and large wingspan configuration can get the desired steep, slow climb but hurt cruise performance. Increasing wing loading and adding a high lift system makes more power and possibly a constant-speed prop necessary for enough power to climb. In the process, cruise performance is significantly improved.

Short Landing

Like the takeoff, the landing maneuver has two segments: the final approach over the obstacle and the ground roll after touchdown. The keys to achieving the short landing part of STOL are slow approach speed and the ability to fly a steep approach. While a big engine and lots of thrust can haul an airplane out of a short field, landing is almost completely dependent on the performance of the wing and high lift system.

Approach: During final approach the plane must clear an obstacle and then descend to the ground. For a STOL mission, the final approach should be both slow and steep. The steep approach is needed because small landing spots are most often surrounded by large obstacles such as trees. As with takeoff, the goal is to minimize the total distance from the obstacle to the point where the airplane comes to rest on the ground. It does little good to be able to stop short after touchdown if you need a long clear area for your approach, and flying through the trees is not recommended.

To approach steeply the plane must have a lot of drag in its final approach configuration. This is needed for two reasons. First, the slope of the final approach is controlled by the lift-to-drag ratio of the airplane. If L/D is high, the approach will be shallow, so a low L/D is needed. Lift must equal weight, so the only way to reduce L/D is to add drag. High drag is also desirable in the flare to keep the airplane from floating. As the airplane enters ground effect the induced drag drops, and the airplane will tend to float. A low-drag airplane can cover a lot of ground sitting in ground effect a few feet above the ground during the flare. Some extra drag to slow the airplane when the nose is raised to flare is desirable.

The primary source of extra drag to steepen the approach slope is the flaps. Most of the stall speed reduction from flaps comes from the first 20 to 30 of deflection. Greater deflections are used primarily to add drag to get a steeper approach. High-drag flaps are good for landing approach, but can be a problem in a go-around. During a missed approach, the engine must have enough power to arrest the descent, and then establish a positive rate of climb starting with the airplane in the approach configuration at approach airspeed. For lower-powered airplanes this can be a problem, as the engine must overcome the extra drag of the flaps and accelerate the plane to an efficient climb speed.

Another good source of drag for steep approaches is a set of spoilers, which has two advantages. First, spoilers can be retracted quickly to clean up the airplane for a go-around. Second, they can be deployed fully on the ground to dump lift after touch-down to aid braking.

Ground roll: After the airplane touches down, it must stop. For short landings, a slow touchdown speed is a must because the amount of braking force available to stop the airplane after touchdown is limited. Also, the same speed-squared effect is present on braking as it is during the takeoff acceleration. The distance required to stop varies as the square of the touchdown speed.

The braking force available is directly proportional to the amount of weight on the wheels. After touchdown, it is desirable to transfer load from the wings to the wheels quickly. Landings with little or no flare help to accomplish this. Rapid retraction of the flaps after touchdown also helps.

Barnaby Wainfan is a principal aerodynamics engineer for Northrop Grumman’s Advanced Design organization. A private pilot with single engine and glider ratings, Barnaby has been involved in the design of unconventional airplanes including canards, joined wings, flying wings and some too strange to fall into any known category.

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