Sunday, November 14, 2004

Oh, What a Lucky Man I Am, Part 2

Part One of this multi-part series of posts is here.

Before I talk about the actual flight I took last Friday, I want to go over a couple more technical aspects of airplanes. That will allow my narrative to flow better, once I get to it.

In the previous post, I talked about the three engine control levers, with a focus on the blue propeller control lever. This time, I’d like to talk more about the throttle. A piston engine is basically a glorified air pump. It sucks air in through the air filter, past the throttle plate, and into the cylinders, where it is mixed with fuel, compressed, and ignited. The extra pressure caused by the heat and chemical change of combustion drives the crankshaft and the propeller, with the burnt gases pumped out through the exhaust pipe. When the throttle is closed (the black lever pulled all the way back), the throttle plate almost completely blocks the intake manifold, letting relatively little air into the engine, thereby limiting the power produced. When the throttle lever is full forward, the throttle plate is turned edge on to the air flow so that there is no constriction blocking air flow to the engine allowing full power to be developed. Intermediate throttle lever positions yield intermediate power levels.

How does the pilot know how much throttle he has set? There is a pressure gauge at the downstream side of the throttle valve. Because the engine is acting as a pump, a closed throttle results in a partial vacuum at the pressure gauge, while a wide-open throttle results in near-atmospheric pressure. When the engine is not running, there is no pumping action, and therefore no pressure drop at the gauge no matter what the throttle is set at, so the gauge indicates full atmospheric pressure.

Atmosperic pressure is measured for scientific purposes in a unit such as pounds per square inch (psi). At sea level, atmospheric pressure is about 14 psi. The manifold pressure (MP) gauge is calibrated a little differently than this. The scale used is the height of a column of mercury that can be supported at the measured pressure. For example, at sea level, the ambient air pressure can support a column of mercury 30 inches high. We say that the pressure is “30 inches Hg” (‘Hg’ is the symbol for mercury). The pilot refers to throttle settings as “inches”. For example, a pilot might say, “I use a cruise setting of 24 inches and 2300 RPM.” During a sea level takeoff, with the throttle wide open, the air filter and intake manifold present enough of a constriction to the air flow that the MP gauge will register about 29 inches.

When the airplane climbs higher into the thinner air, the pilot opens the throttle more to maintain power. For every thousand feet of altitude gained, the engine loses about 1” of manifold pressure, so the pilot must open the throttle more during the climb. At around four or five thousand feet the throttle is all the way open, and any more climbing results in a loss of horsepower. There are other compensating factors, such as less drag from the thinner air, as well as less air pressure working against the exhaust gases, as well as less drag on the propeller. This means the plane has its fastest performance at about 7500 feet. Lower than this, the plane has plenty of power but too much drag, higher, the engine is losing too much power to keep top speed. If you’ve ever driven a car up in high mountains, you know how much power an engine can lose!

So enough about the engine! How does the plane actually fly? In the final analysis, an airplane is simply a stabilized “air ram”. It uses the action-reaction principle of Newton’s third law of motion (for every action there is an equal and opposite reaction). This principle can be illustrated by putting on some ice skates, getting out on a rink, and throwing a nice, heavy medicine ball. The ball will go forward some distance, but you will go shooting backwards! By giving air a shove downwards as they move forward through it, the wings of the plane in turn receive a compensating shove upwards, enough to support all the weight of the plane, allowing it to fly.

For a fixed surface area and air density, the lift a wing generates is proportional to how tilted the wing is (this is called the angle of attack), and to the square of the airspeed over the wings. To illustrate the angle of attack idea, extend your arms out horizontally, with palms parallel to the floor. If you keep your fingertips pointing in the same direction and rotate your hands so that your thumbs move toward the ceiling, you are increasing the angle of attack. You can experience how the usable force that moving air contains is dependent on the square of the airspeed the next time you are in a moving car. Put your hand out the window and tilt it to maybe a 20 or 30 degree angle of attack. At 15 mph, there is not much force on your hand. At 30 mph, there is four times the force, and at 60 mph, there is 16 times the force! Who hasn’t ever put their hand out the window at 70 mph, and fiddled with the angle of attack to make their arm go up or down?

Because of the dependency of lift on these two different factors, a plane can fly at many different speeds. If I’m flying straight and level at full cruise speed and want to slow down (which I do when maneuvering near an airport, site seeing, or am getting hammered by turbulence), I throttle back. This reduces thrust from the propeller, which means I am no longer compensating for all the drag at that speed. As the plane slows down to a speed where drag once again equals thrust, the airspeed over the wings decreases, and I compensate by pulling back on the wheel (actually it’s called a yoke) and pitching the nose of the plane to a higher angle above the horizon. This increases the angle of attack of the wings thereby keeping the total lift force constant. Now I am straight and level at a slower speed. It takes a while to learn how to do all of this smoothly and intuitively, but eventually it all becomes automatic.

Now there is a limit to how slow I can fly. Obviously, I can’t slow down to zero airspeed with the nose pointed straight up! It’s an airplane, not a helicopter! So where is this limit hit? It happens at an airspeed called the “stall speed”. At this airspeed, I’ve tilted the wing to such a high angle of attack that the air can no longer follow the top surface of the wing (think about it; if you were in a car, and stuck your hand out the window palm forward, would you really expect the air to do a 90 degree turn to flow down the back of your hand?). It turns out that air will only follow the wing at an angle of attack below 16 to 18 degrees. Below the stalling angle of attack, the air flows nice and smoothly over the top surface and is ejected at the trailing edge with some downward momentum due to the tilt of the wing. But once you hit the stalling angle, the airflow separates from the surface, is no longer steered downward, and suddenly most of your lift goes away. A pilot only intentionally stalls a wing when doing aerobatics (I haven’t had any aerobatic training), when practicing basic maneuvers at a safe altitude, or during the landing flare close to the ground (I’ll describe how that works in the narrative section of these posts). If a pilot accidentally lets the airspeed get too slow when maneuvering at low altitude near an airport and causes a stall, he generally doesn’t survive. A stalled (I’m talking about wings stalling here, not engines) airplane is no longer stable and it takes full attention to keep the plane flying straight. A situation that results in an accidental stall quite often results in a spin, to boot.

One final point of aerodynamics. Above stalling speed, a pilot can trade between angle of attack and airspeed to keep the plane in the air. At high airspeed (while cruising), the wing is encountering a very large volume of air and giving it a fairly gentle push. At low airspeed (a bit above the stall), the wing is encountering a lower volume of air, and giving it a much more violent shove. To get a bit scientific, in order to lift the plane, the wings must generate a certain amount of lift force. From Newton’s second law of motion, this force is equal to the mass of air shoved per second times the velocity at which it is shoved downward. So at high speed the mass is large, but the shove velocity is low, while at low speed the mass is small but the shove velocity is high. Now, the air that is being shoved is being given a certain amount of energy. This is equal to the mass of the air times the square of the downward shove velocity. Because the energy given to the air (which has to come from somewhere, so it is felt as an “induced drag” force on the airplane itself) increases so strongly with increased shove velocity, this means that the induced drag is greatest at low airspeed when the wing is giving a huge shove to a relatively small amount of air. So induced drag increases the slower the plane goes. The plane is also subject to the more familiar kind of drag (called parasitic drag) that results from moving quickly through the air, the kind that is experienced by a car or a person on a bicycle. This type of drag increases the faster the plane goes. The total drag is the sum of the induced and the parasitic drag. So the curve of total drag vs. airspeed has a ‘U’ shape to it. At the bottom of the ‘U’ is the point of minimum drag. This is the airspeed at which the plane stays in the air with the least expenditure of power. Any amount of engine horsepower available above this amount can be applied to increasing the plane’s altitude. The fastest climbs are done at this airspeed. The Trinidad has a stall speed of 70 knots, a best-climb speed of 95 knots, and a maximum cruise speed of 160 knots (a knot is 1.15 mph).

Okay, one last technical point. The slowest a plane can fly is the stall speed. For takeoffs and landings, it is desirable that this speed be as slow as possible in order to minimize the amount of runway required, and for safety (since when landing, the wheels touch down at about stall speed; it’s always nice to minimize the amount of kinetic energy when coming in contact with the ground!). Most airplanes have wings that can change their configuration by lowering flaps at the trailing edge of the wing. Imagine a dollar bill as being a wing. If you make a downward fold parallel with the long axis of the bill, about one fifth of the way forward from the back edge of the bill, you’d have a good approximation of the typical flap geometry. The flaps do a couple of things. Because the air wants to follow the top surface of the wing, dropping flaps allows there to be a vastly increased downward flow of air behind the wing at angles of attack much less than the stalling angle of attack. In fact, with the flaps lowered, the lift can be greater than the unflapped wing could ever achieve, even at the stalling angle of attack. The extra lift means that the air doesn’t have to flow over the wing as quickly in order to hold the plane in the air. For the Trinidad, the stall speed with flaps is 59 knots, 11 knots slower than the unflapped stall speed. That’s 30% less kinetic energy at touchdown.

Because lowered flaps result in a much stronger downward shove of the airflow, the drag is greater. The Trinidad has three flap settings: retracted, approach (a 10 degree angle), and landing (a 30 degree angle). The approach setting serves to lower the stall speed and add some drag, and the landing setting serves to add a huge amount of drag, because the flap surface area hanging under the wing and facing the oncoming airflow acts as an air brake. When you’re landing an airplane, the whole job is to safely get rid of all your energy, both in terms of speed and altitude. The flaps help greatly to shed all of this energy. Additionally they allow a steeper descent to the runway, which helps in clearing obstacles in the approach path (it’s no different than a car: brakes let you go down a steeper hill than you safely could otherwise).

Okay, I hope that all made sense. With the technical background out of the way, I can finally talk about my flight in the next post of the series!

To be continued…

Update: Part 3 of the series is here.


Anonymous said...

This may be a nitpick, but I'm studying for my CFI written right now (book a few feet from me), and I have a different interpretation of this event:

This reduces thrust from the propeller, which means I am no longer compensating for all the drag at that speed. As the plane slows down to a speed where drag once again equals thrust, the airspeed over the wings decreasesThis couldn't happen.

The elevator is trimmed for a certain AoA, thus trimming the wing for a certain AoA.

When power is reduced, the plane slows down a tiny bit. Drag is now greater than thrust. However, the wing also produces less lift, and so the airplane begins to fall.

As the airplane falls, air hits the wing from below, thus increasing the AoA, and the airplane picks up horizontal speed, thus increasing lift. The plane will continue pitching down, and accellerating downwards, until the wing is producing the same amount of lift it was before the power reduction, and the torques of wing and elevator are balanced.

The airplane won't slow down to where drag is equivalent to thrust, because then lift and weight would be unbalanced.

Matteo said...

It's nice to have a fellow pilot reading! Yes, I know that technically the airspeed over the wings would not decrease, but the plane would descend. However, I predicated my description on the idea that I'd be applying back pressure and up trim to maintain altitude as the plane slowed down. That's why I said:

"I compensate by pulling back on the wheel (actually it’s called a yoke) and pitching the nose of the plane to a higher angle above the horizon. This increases the angle of attack of the wings thereby keeping the total lift force constant. Now I am straight and level at a slower speed. It takes a while to learn how to do all of this smoothly and intuitively, but eventually it all becomes automatic."

There will be a few imprecisions in my descriptions, since I am writing for non-pilots (if I was going to be absolutely precise, I'd have to write an entire book!).

Thanks for your comment, and for reading my blog. Good luck on your CFI exam!