By the Book

Takeoff performance planning

June 1, 1992

Ask most pilots about the importance of takeoff performance planning, and they will likely nod in the direction of density altitude, acknowledging the toll on performance that hot days and high altitudes can extract. Then ask them about the takeoff performance of their own airplane on a "standard" 59-degree-Fahrenheit day. They gaze over at the runway, mentally estimate where they usually become airborne, and mutter, "Oh, about 1,700 feet, I guess." And over the mythical 50-foot obstacle? "Well, maybe another 500 feet," they say.

They may be right. Then again, they may not. If any doubt exists that most pilots do not bother to compute how their airplanes will behave in any given set of environmental conditions, a look at the safety statistics will quickly reveal the truth. Almost a quarter of all flight emergencies, according to AOPA Air Safety Foundation figures derived from National Transportation Safety Board reports, begin during the takeoff and climb phases of flight, often due to factors that should have been taken into account before the pilot climbed into the cockpit. Only landing emergencies are more prevalent.

Of course, pilots are responsible for computing takeoff performance. But they are often not given very good tools to work with in making such computations. Particularly in the days before pilot's operating handbooks became more or less standardized, the documentation available to the pilot was often of very limited value. The manual for the 1967 Cessna 150, for example, offers one takeoff distance table that assumes takeoff at maximum takeoff weight (1,600 pounds) with flaps retracted from a "hard-surface runway." Three headwind components are offered0, 10, and 20 mph-and four altitudes-sea level, 2,506, 5,000, and 7,500 feet.

Two footnotes offer a little more: "increase the distances 10% for each 35OF increase in temperature above standard for the particular altitude," and "For operation on a dry, grass runway, increase distance (both 'ground run' and 'total to clear 50-ft obstacle') by 7% of the 'total to clear 50-ft obstacle' figure." Okay, so what's required on a 720 day at 4,300 feet with a 17-mph quartering headwind? In an airplane weighing 1,300 pounds? In tall grass? Quick now.

We shouldn't single out Cessna, however. A Cherokee 140 manual of the same vintage offers a graph of takeoff distance versus density altitude. On the one hand, computing density altitude-a simple task with any flight computer-eliminates the requirement for complex interpolation of altitude and temperature. On the other, we are left to assume that Piper's engineers assumed maximum takeoff weight and a dry, paved runway. Plus, wind and other factors cannot be accurately accounted for. Too many assumptions.

Well, we say, these airplanes are trainers, and part of training is to experience the effects of nonstandard conditions on aircraft performance. Perhaps. Wobbling off the runway and mushing into the trees is sure to be a powerful learning experience. But while more complex airplanes often came with better documentation, and POHs improved considerably with the years, we still don't get everything we need to satisfy ourselves that we can take all the variables into account. The 1976 Beech F33A Bonanza POH, for example, admirably allows us to account for density altitude (without having to compute it), takeoff weight, wind, and obstacle height. But factors such as runway slope and surface are still left to conjecture.

What's a pilot to do? First, we can turn to rules of thumb. Aerospatiale's 1986 TB-10 Tobago POH doesn't offer much more than the 1967 Cessna book (it even leaves out wind effects), but it does tell us that "rolling distances at takeoff shall be increased by10% on tarred runway; 17% on hard grass; 20% on short grass; 37% on high grass; more than 37% on soft, muddy, or snowy field." Those are pretty conservative numbers, but we should also acknowledge that unpacked snow or slush can be expected to at least double takeoff distance. Our best bet is to make a conservative estimate, tack on another 50 percent for the spouse and sprouts, and remember one more rule of thumb (this one from James Embree's excellent book, The Axioms of Flight): Abort the takeoff if 70 percent of takeoff velocity is not attained within 50 percent of available runway. Obviously, some runway conditions could make it impossible to ever reach flying speed.

Embree's book, which we've mentioned before in this column, is particularly useful to those of us flying airplanes for which documentation is marginal. To take airplane weight into account when using the Cessna or Piper manuals mentioned above, for instance, Embree suggests that takeoff distance varies at least as much as the square of the weight difference. To take our hypothetical Cessna 150 question as an example, we'd divide the actual weight by the published (max gross) weight (1,300/1,600 = 0.8125), square it (0.66), and multiply that by the published distance. In this case, if we're being very conservative, we'd just stick with the published distance, but it's useful to have some benchmark. Why? Because we're often told that, under high density altitude conditions, it may be necessary to wait for better conditions or to reduce our takeoff weight. This equation gives us a way to estimate how much weight we must remove. Again, the truly cautious pilot would want to add a safety margin of 50 percent.

If the POH does not provide adequate information regarding the effect of a headwind on takeoff distance, it can be very conservatively estimated by first determining the strength of the wind relative to the takeoff airspeed of the airplane (e.g., 17-knot headwind divided by 65-knot takeoff speed = 0.26) and then reducing the no-wind takeoff distance by that factor.

For any wind not straight down the runway, it will naturally be necessary to use the wind side of our flight computer to determine how much is headwind and how much is crosswind. How much crosswind can your airplane accommodate? Multiply its stall speed in the landing configuration, V so, by 0.2. Many airplanes can tolerate significantly higher crosswinds, but that's a good, safe number because it's a minimum certification standard of most light airplanes.

Another factor that influences takeoff planning is runway slope, or gradient. Runway gradient is depicted on the airport plan view on instrument approach plates and is noted in the Airport/Facility Directory if it is 0.3 percent or more. If you know the length of a runway and the altitude of each end, you can estimate the gradient (assuming the slope is constant): Divide the height difference by the length in hundreds of feet. A 2,000-foot runway that rises 30 feet from one end to the other has a gradient of 30 divided by 20 = 1.5 percent. The effect of runway slope on takeoff performance is not linear, so there is no easy formula to apply. As a rule of thumb, however, we should probably avoid runways that slope up at more than half the best climb gradient of the airplane we're flying under existing density altitude conditions. We can estimate the best climb gradient by dividing the rate of climb by the best climb speed in miles per hour. A rate of climb of 400 fpm at a speed of 90 mph, for example, yields a climb gradient of just under 4.5 percent. This formula comes courtesy of the makers of the Topcomp takeoff performance computer, which we'll discuss in a minute.

Climb gradient should continue to concern us after we're clear of the runway. Taking off from Denver under standard-day conditions, our 1967 Cessna 150 climbs at 370 fpm at an airspeed of 69 mph. Assuming no wind, this yields a climb gradient of a little over 320 feet per statute mile. Fair enough, but suppose we're making this same takeoff in a 1966 Piper Aztec and suffer an engine failure shortly after takeoff. Our climb rate of about 50 fpm at our single-engine best rate of climb speed of 100 mph yields a breathtaking 30 feet of altitude gained per statute mile. And that's assuming we managed to get our gear up. We'd best be pointed east. (You can determine gradient in feet per mile by setting the speed index of your flight computer. [the "60" mark] opposite your groundspeed; then simply read the gradient in feet per mile on the inner scale opposite the climb rate in feet per minute on the outer scale. Just remember that if your speed is measured in knots, the gradient is in nautical miles; if it's in miles per hour, the gradient is in statute miles.)

A moment ago we noted in passing that rate of climb has to be adjusted for density altitude (and weight), just as takeoff distance does. Again we're faced with a problem with older aircraft documentation that solves for only one weight and/or forces us to interpolate for density altitude. The Cessna manual does offer this: "Decrease rate of climb 15 fpm for each 10° F above standard-day temperature for particular altitude." But many older manuals don't provide standard temperature tables, so we simply have to remember that standard temperature is 59F (15'C) at sea level and that the standard temperature lapse rate is 3.5° F (2° C per thousand feet of altitude. Better idea: Photocopy the international standard atmosphere (ISA) graph out of a current POH. If we need performance: This time, we divide the published (max gross) weight by the actual weight (using our Cessna again, 1,600 / 1,300 = 1.23), square it (1.5), and multiply that by the published rate of climb at max gross.

Some alternatives to number crunching are available to the pilot who takes takeoff performance planning seriously. One is the aforementioned Topcomp, a slide-rule sort of thing with six sliding scales. First, set the temperature in a window. Then set an index mark opposite the pressure altitude. Continue by positioning the slides to mark current conditions of runway surface, slope, wind, airplane weight, and standard-day max gross weight. Finally, you read off the required takeoff distance from the bottom scale. A window displays the percent of standard-day sea-level rate of climb achievable at any given pressure altitude. Topcomp is remarkably accurate for both fixed-pitch and constant-speed single- and twin-engine normally aspirated airplanes if the instructions are followed. (Special instructions apply for turbocharged airplanes.)

Another alternative is the SanTech FDF-26 density altitude performance computer. The front is a standard flight computer that allows you to solve for true airspeed, density altitude, and corrected altitude, plus time/ speed/ distance and other sliderule math. On the back side, you set temperature into a window and then read a multiplication factor for takeoff performance and a percent factor for rate of climb in two other windows opposite the appropriate pressure altitude. This computer also solves for both fixed-pitch and constant-speed propeller-driven airplanes.

Topcomp ($17.50) and the FDF-26 ($9.95) are available from Skyline Pilot Supply (telephone 800/327-4586) and other aviation supply houses. The Axioms of Flight ($19.95) is available from Flight Information Publications (telephone 314/469-1488).

As handy as mechanical flight planning aids are, however, they must be backed up by the pilot's familiarity with his airplane's performance data (sketchy though the figures may sometimes be), a solid understanding of the effects of nonstandard conditions on aircraft performance, and the skill and proficiency to fly the airplane by the numbers.