# Efficiency: Slow Burn

## Quick calculations for fuel conservation

You’ve encountered a stronger-than-expected headwind on a long flight and want to reduce your fuel burn to ensure you arrive at your destination with adequate reserves. You’re about two-thirds of the way to your destination, and it’s the nearest airport, so you can’t divert or turn around. The mixture knob is as far out as it can go for the leanest possible fuel/air mixture. You’re flying VFR as high as the cloud ceiling allows for the best possible true airspeed.
Illustration by Eva Vasquez

You know your airplane’s longest range in no-wind conditions can be had by flying at the maximum lift-over-drag point on the total drag curve. But that number isn’t marked on airspeed indicators, and these aren’t no-wind conditions. How fast should you fly to ensure you complete the flight while burning the least amount of fuel?

Aeronautical engineers are wizards at coming up with complex mathematical formulas for aircraft performance—but all those numbers and symbols can be devilishly difficult to put into practice. Fortunately, there are some straightforward guidelines to follow, and they aren’t much harder than figuring out the proper tip to leave for the waiter at an airport restaurant.

First, your airplane’s maximum lift-over-drag speed (L/D Max) is the same as its best glide speed. Say you’re flying a Citabria 7GCBC with a best glide speed of 78 mph IAS. In no-wind conditions, you could slow to 78 mph, lean aggressively, and know that you were maximizing range while minimizing fuel consumption. But you’re also dealing with a 30-mph headwind, and slowing to L/D Max would slow your groundspeed to a crawl and expose you to the headwind for much more time. Better speed up by some amount, but how much?

Simply add the strength of the headwind (30 mph) to your best glide speed (78 mph) and you’ve got the most efficient speed to fly—here, 108 mph.

To determine an airplane’s Carson speed, multiply its best glide speed by 1.32. This will get the best result in terms of true airspeed and fuel consumption.Flying at L/D Max seems excruciatingly slow—because it is—and pilots are typically loath to fly at such paltry speeds. Luckily, there’s another theoretical speed that’s highly efficient in terms of both fuel and time, and it’s called the Carson speed in honor of aerodynamicist Bernard H. Carson, who first defined it in 1980.

Carson, who taught at the U.S. Naval Academy for 32 years, called his idea the “least wasteful way of wasting fuel,” and he showed that a 32-percent increase in airspeed above L/D Max is available for a measly 16 percent rise in fuel consumption. In aerodynamic terms, that’s cheap speed.

Increase your airspeed beyond 32 percent, however, and it quickly turns into a raw deal. The total drag curve steepens, and each additional knot becomes more expensive in terms of fuel consumption.

To determine an airplane’s Carson speed, multiply its best glide speed by 1.32 (to increase it 32 percent). Going back to the Citabria, a best glide speed of 78 mph times 1.32 equals 103 mph. So 103 mph is the optimum airspeed—and flying at the highest possible altitude at which your Citabria can deliver 103 mph IAS will get the best result in terms of true airspeed and fuel consumption.

Also, headwinds matter here, too, so the Carson speed changes with headwinds and tailwinds. If the headwind or tailwind component is 10 knots or less, don’t bother. It’s academic. In stronger winds, however, the Carson speed increases about one-third of the headwind component, and it decreases by the same fraction in a tailwind.

For math majors, there’s a vast repository of complex formulas to back this stuff up. For the rest of us, best glide plus 32 percent gets excellent fuel efficiency at a reasonable speed.

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#### Dave Hirschman

AOPA Pilot Editor at Large
AOPA Pilot Editor at Large Dave Hirschman joined AOPA in 2008. He has an airline transport pilot certificate and instrument and multiengine flight instructor certificates. Dave flies vintage, historical, and Experimental airplanes and specializes in tailwheel and aerobatic instruction.