“Is there a way to compute the strength of up- and downdrafts based on the amount of increase or decrease in airspeed? If I’m cruising along at an indicated 135 knots with a constant power setting, maintaining altitude and see my airspeed decrease to 110 knots as I pitch up to overcome downdrafts while maintaining altitude and power, it seems there should be some way to calculate the strength of those downdrafts based on the loss of airspeed. Coming out of the downdraft and into an updraft would have the reverse effect, with maybe 155 knots or so the resulting airspeed as the airplane pitches down to maintain altitude. I thought this might be a simple right-triangle problem, but the more I think about it, the more it seems like it’s probably more complicated than that.”
Actually, it’s less complicated than that.
What we call an updraft or downdraft is a movement of air within a larger air mass that is sufficiently large or continuous for an airplane to remain in it for a while. Flying parallel to a mountain ridge, a sailplane may remain in such a movement for hundreds of miles, like a surfer sliding downward yet always remaining in position on the face of a rising wave. That’s an extreme case, but generally speaking, the difference between an updraft and a “bump,” or a downdraft and what some people call an “air pocket,” is nothing more than duration.
What you feel as an updraft or downdraft is not necessarily a vertical movement of the surrounding air. The air can be going any which way, but you experience just the vertical component of its movement. What my correspondent calls the “strength” of the draft is the vertical velocity it imparts to the airplane if you allow the draft to carry you with it. Many pilots consider it a matter of honor to hold altitude accurately, however, and under IFR you are required to do so.
If you leave power alone but maintain altitude when you encounter rising air, you will gain speed. My correspondent’s question amounts to: How much speed will I gain for a given updraft? The answer will depend on both the weight and the aerodynamic cleanness of the airplane, but the relation between speed and updraft strength in any particular case is basically straightforward.
Suppose the airplane is a Skylane and weighs 3,000 pounds. To maintain a constant altitude in a 1,000 fpm updraft is equivalent, from the airplane’s point of view, to descending 1,000 fpm in still air. Now, as far as power is concerned, climbing and descending are two sides of the same coin. You have to employ power to climb — that’s perfectly obvious — but what may be less intuitively obvious is that descending gives back power at exactly the same rate. That’s why the airplane accelerates when you put the nose down; it’s just as if you increased the power output of the engine.
The power released by a 3,000-pound airplane descending 1,000 fpm is roughly 91 hp. This number is easily arrived at because 1 hp is defined as the power required to raise 33,000 pounds 1 foot in one minute; therefore, 3,000 multiplied by 1,000, divided by 33,000, is about 91.
Now, let’s say the airplane was cruising at 70 percent power. Assuming the propeller converts about 85 percent of engine power into useful thrust, it was expending 235 times 0.7 times 0.85, or 140 “thrust horsepower” in order to cruise at an indicated 135 knots.
Adding the gift of 91 hp to that means increasing the thrust power available by 65 percent (it’s not necessary to correct the 91 hp for propeller losses, since it’s not passing through the propeller). Now, as a rough rule (and one that applies only at higher speeds), speed is proportional to the cube root of power. The cube root of 1.65 is 1.18; 1.18 times 135 knots is 159 knots. So we would expect this particular airplane to accelerate to 159 knots in a sustained updraft of 1,000 fpm. Actually, this isn’t quite right because the power required is partly proportional to the indicated airspeed and partly to true airspeed. But the cube rule is only approximate in the first place; this is just a back-of-napkin calculation.
In practice, if you maintained altitude, you would not know the velocity of the updraft, only the speed gained; but you can equally easily work the problem backward. Let’s say you’re cruising at 135 knots, and you find yourself in a sustained updraft. You trim to maintain your assigned altitude, and the indicated airspeed increases to 145 knots. What is the “strength” of the updraft?
Your speed increased by 14 percent; the cube of that ratio is 1.48. You were using 140 hp to cruise, and the updraft has given you a 48 percent increase, or 67 hp; 67 hp times 33,000 is 2,211,000. Dividing by the weight of the airplane, or 3,000 pounds, we get 737 fpm as the speed of the updraft.
The same reasoning applies to a downdraft, keeping in mind that at lower speed the cubic relationship between power and speed becomes less and less valid.
Suppose you find that you must slow from 135 to 125 knots to maintain height in a downdraft. The new speed is 93 percent of the old; cubing that number, the power required to cruise in smooth air at this speed is around 80 percent of what it was before. By slowing down, you have made the difference in power — 20 percent of 140, or about 28 hp — available for climbing through the downdraft. Doing the horsepower math again tells us that the speed of the downdraft is around 300 fpm (28 times 33,000, divided by 3,000).
These calculations are simple because the underlying physics is simple. Vertical speed and horsepower are fungible. (My contract allows me one weird word per article; this one means “interchangeable.”) An airplane’s rate of climb at any given speed is simply the equivalent, in pounds of airplane mass and vertical speed in feet per minute, of the difference between the horsepower required to maintain level flight and the horsepower available from the engine or from vertical movement of the surrounding air.
Just one question: Why would you want to know this?
Well, suppose you were at the airport cafe one rainy weekend day, nobody was flying, and one of your friends put down her beer and asked: “Is there a way to compute the strength of up- and downdrafts based on the amount of increase or decrease in airspeed? If I’m cruising along at an indicated 135 knots with a constant power setting, maintaining altitude and …”
