# Tabulating Takeoff

###### Peter Garrison

Galen Hanselman, who has published several guidebooks and charts for pilots interested in landing on something other than 5,000-foot paved runways, sent me his two-volume flier's guide to Utah and the associated "Supplemental World Aeronautical Chart," which resembles a WAC chart but includes a slew of backcountry airstrips not on the WAC. The quality of his productions and the effort he has put into them are impressive. One volume of each set covers the airstrips themselves in great detail, with frank and often rather disconcerting commentary about their condition and risks; the other concerns why you would want to go there — history, lore, hikes, scenery, fishing and so on.

I exchanged a few emails with Hanselman, and at one point he commented that he wished he had something more to tell his readers about effects on takeoff performance of wind, altitude, runway gradient, surface and so on than just the rules of thumb found in the late Sparky Imeson's Mountain Flying Bible, which is, if you'll pardon the redundancy, the bible of mountain fliers.

I responded that I had a computer program for calculating takeoff distance that incorporated those variables and more, and I ought to be able to come up with something.

Ah, the vanity of human wishes! It turns out takeoff distance is very difficult to calculate with anything like precision. And, for that matter, how would you know you had the answer right? The best you can hope for is to simulate a few existing airplanes and see how well your results match the charts in the POHs.

Here's how the program works. At intervals of a tenth of a second it calculates thrust, subtracts resistance due to friction, drag and runway slope, and applies what's left to the mass of the airplane. This results in an acceleration and a certain distance traveled. The process repeats itself, pouring out speed, distance, acceleration, lift and so on at one-second intervals until the virtual airplane reaches its takeoff speed.

The procedure is pure physics and ought to work fine. What goes wrong is the data. Garbage in, garbage out. Thrust and friction cannot be known with precision; each type of propeller has its own characteristics, each backcountry airstrip surface is unique, each pilot handles his airplane in his own way, and many of the doubtful variables influence one another.

It often happens, however, that even when a computer simulation gets the wrong answer it may still teach us something new or call our attention to something we've overlooked.

For example, if I vary the time to full power between zero and, say, seven seconds, I see very little difference in takeoff distance. Why? Well, it's common sense, really: The airplane is moving very slowly at the start of the takeoff roll, and so it doesn't cover much distance in the first few seconds no matter what you do with the throttle. A rolling takeoff may help you avoid getting bogged down in soft soil or sucking up pebbles into your prop, but it won't make a noticeable difference in where you leave the ground. On the other hand, running up to full power while standing on the brakes allows you to adjust the mixture for best power.

Since the airplane is moving fastest at the end of the takeoff roll, the takeoff distance is going to depend heavily on the liftoff speed. For instance, rotating a Skylane at 60 knots rather than 55 (those are calibrated airspeeds; the Skylane's airspeed indicator is way off) lengthens the takeoff roll by 25 percent.

The influence of aerodynamic drag is relatively small. Thus, delaying flaps until late in the takeoff roll doesn't make much difference. Surprisingly, too, although there is an "optimum" compromise between increased drag and reduced friction when you hold the nose up for a "soft field takeoff," the effect on distance is again small, except to the extent that holding the nose up tends to get you airborne at the earliest possible moment.

The thing to bear in mind about getting airborne at a very low speed is that you may be unable to climb until you have gained more speed in ground effect. The takeoff roll may be shorter, but the distance to clear an obstacle is no different.

The big factors in takeoff distance are the ones you'd expect: density altitude, weight, wind, surface condition and gradient.

For unturbocharged airplanes, density altitude reduces the power and thrust available and therefore the rate at which the airplane accelerates. According to the program — your results may vary — takeoff distance increases by about 8 or 9 percent for every 1,000 feet of density — not pressure — altitude. You can find presumably exact information about density altitude and weight in the POH, so it's not necessary to memorize any rules of thumb. Weight is a critical factor because it affects both acceleration and liftoff speed. The Skylane POH, for example, shows the airplane rotating 5 knots slower at 2,400 pounds than at 2,950 and getting off the ground, at sea level, in 440 feet rather than 705.

The Skylane POH says to reduce takeoff distance by 10 percent for every 9 knots of headwind. That's a useful rule of thumb, but couldn't they both be 10? (Obviously it goes astray in really strong winds, since a Skylane's takeoff distance would be zero in a 55-knot wind.) Tailwinds are a more sensitive matter, since they increase the liftoff groundspeed and so make the airplane eat up more runway at the departure end of its roll. The Skylane book says to add 10 percent for every 2 knots of tailwind, which seems extreme; a Mooney 231 chart shows a 26 percent increase for a 10-knot tailwind. My program predicts a 34 percent increase for a 10-knot tailwind for a hypothetical Skylane-like airplane. So you see we're all over the map.

Various kinds of runway surfaces present different resistances to the rolling airplane, but it's impossible to categorize surfaces in any precise way. My program shows a 50 percent increase in takeoff distance for a "soft" field, and 20 percent for "grass" — not to be confused with "turf" (around 5 percent). But how soft is soft, and how tall is grass? My program also has a quicksand setting: The airplane does not move at all.

Unlike surface condition, runway gradient can be specified very precisely. Hanselman has personally measured the slopes of all sorts of godforsaken landing strips, no more than paler places in the sagebrush, and reports them to two decimal places. But then what? And, more troublingly, what if the wind is blowing downhill?

Well, here's what the computer has to say. If you're taking off with a 5-knot wind at your back, you'll need a 5 percent downslope to get off the ground in the same distance as you would from a level runway with no wind. Oddly enough, it works the other way around too: A 5-knot headwind cancels the effect of a 5 percent upslope. This can't be a general rule, though; it's too simple.

When you take off with a tailwind your climb gradient will be unexpectedly shallow. Be aware of obstacles ahead that you would normally expect to clear; a tailwind may carry you into them.

A simple rule to remember — call it the two-thirds rule — is that the second half of your takeoff distance will take half as long to cover as the first, but you'll travel twice as far gaining the second half of your takeoff speed as you did the first half. For example, if your takeoff roll is 600 feet and you lift off at 50 knots, you will have reached 25 knots in only 200 feet, but if it takes you eight seconds to reach the 300-foot halfway mark, it will take only another four seconds to cover the remaining 300 feet.

That is why some pilots use a simple go/no-go rule for tight takeoffs. If you don't already have more than two-thirds of your liftoff speed when you reach the midpoint of the runway, abort the takeoff. There's not enough time left for thinking it over.

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Peter Garrison taught himself to use a slide rule and tin snips, built an airplane in his backyard, and flew it to Japan. He began contributing to FLYING in 1968, and he continues to share his columns, "Technicalities" and "Aftermath," with FLYING readers.