### A Weighty Matter

Here in the USA flight instructor certificates expire after two years. There are several ways to renew; when I was instructing in a charter operation, renewal was a matter of catching the FAA inspector while he was in town, but now I find the most convenient way is through a Flight Instructor Refresher Clinic [FIRC], a 16 hour approved course. The Idaho Department of Aeronautics runs a good one, and Frank Lester rotates them through our rather large state, so everyone gets a chance to attend. Better yet, he offered to let me attend for free in exchange for teaching some of the segments.

When I told my university students that I would spend the weekend attending a 16 hour course they recoiled in horror. When I told them that there would be a test they were impressed.

Usually I believe that what happens in the Pocatello Holiday Inn stays in the Pocatello Holiday Inn, but due to popular demand here are some ideas from my presentation on Weight-and-Balance. The most striking thing to me was the central role of weight in all aerodynamic questions.

**Glider Nerd Calculations**

Consider a 3000 pound airplane in level flight at constant airspeed at 100 knots (true airspeed). A reasonable lift-to-drag (L/D) ratio might be 10; see the graph above, taken from

*The Pilot's Handbook of Aeronautical Knowledge*. In level flight, thrust and drag are equal, as are weight and lift, so we have 3000 pounds of lift. Since L/D = 10, this translates into 300 pounds of thrust or drag, depending on your outlook on life.

An airspeed of 100 knots is just about 10,000 ft/sec, which translates into a (300 x 10000)/33000 = 91 Brake Horsepower required.

Rate of Climb depends on

*excess thrust*. Most people don't appreciate this until they study multiengine aerodynamics, but it applies as well here. The formula is

where

*E*is excess thrust and

*W*is weight. Suppose that the airplane has

140 HP available, which is reasonable for a normally-aspirated engine at altitude. Then the excess thrust is 140 - 91 = 49 HP, and the rate of climb is

Change the weight to 4000 pounds, however; the L/D does not change (it's a property of the wing), and now we have (400 x 10000)/33000 = 121 Brake Horsepower required. The excess thrust is down to 19 horsepower, and the rate of climb becomes 156 ft/min.

Why do multiengine pilots learn this? Take the 4000 pound airplane at 100 KTAS and give it 400 horsepower available; this is about right for a Seneca. When both engines are turning there are 279 HP of excess thrust available, for a whopping 2300 ft/min climb.

*Yee-haw!*But kill one engine and the excess thrust available is now 79 horsepower, and the rate of climb is down to 650 ft/min. This isn't bad (4000 pounds is light for a Seneca), but the drag picture is a lot worse, too, so L/D has gone down and there is even less excess thrust. The point is that

*losing half the power costs you WAY more than half the climb!*

Change the L/D to 8 and the weight to 4500. Now, at 100 knots, the horsepower required goes up to 170; with only one engine turning there are 30 HP of excess thrust, for a rate of climb of 125 ft/min. At 100 knots you travel forward 10,000 feet in one minute, and the climb gradient is an anemic 75' per nautical mile; the climb angle is less than half a degree.

(Why is the elevation relevant? At higher density altitude the same indicated airspeed corresponds to a higher

*true*airspeed, and hence to more horsepower required.)

I took my Multi-engine Instructor flight test in a Seneca on a hot day at about 4500' MSL. Even though it was in a Seneca (so I had sea level power), when I demonstrated an engine failure to the examiner the airplane would not climb. I headed out across the desert and finally found a thermal that took us to pattern altitude. The moral of this story: always think like you have an even number of engines!

Labels: aerodynamics, performance, weight and balance