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The following article was prepared as part of a petition to the National Transportation Safety Board (NTSB) for review of a series of light aircraft accidents which occurred in mountain wave conditions. The article was the basis for a paper published at the American Institute of Aeronautics and Astronautics (AIAA) Flight Dynamics Conference held in Baltimore, MD in August 1995. The complete paper with additional flight test data and illustrations will be made available here as time permits.
Mountain Wave and Speed-to-Fly for Light Airplanes Steven H. Philipson February 28, 1993 Speed-to-fly is a basic precept of soaring flight for unpowered aircraft. The objective in determining this speed is to find the optimal airspeed for maximum glide performance under varying conditions of lift or sink. Use of this concept is not limited to unpowered aircraft however. It is valuable to the pilots of light airplanes as well. In critical flight situations such as encounters with mountain wave downdrafts, correct application of speed-to-fly theory can make the difference between life and death. Background Speed to fly is explained in detail in virtually every textbook on soaring. It is defined in Conway's Joy of Soaring as "The indicated airspeed which produces the flatest glide in any situation of convection without considering the effect of wind." It is obtained for each type of glider by plotting the performance polar (i.e., the sink rate at each airspeed in the glider's operating range) and adding a scale for vertical motion of the airmass. A line drawn from the airmass motion scale to a tangent point on the glider performance curve crosses the airspeed scale at the airspeed that will yield the flatest glide while flying through the airmass (least altitude lost per unit of distance traveled). Such charts are useful for understanding the performance of a glider but are difficult to apply in flight. Various devices have been developed that aid the glider pilot in applying this data, including the MacCready Speed Ring and final glide computers. Glide computers allow the addition of wind speed to the equation to find the speed for the flatest glide over the ground. These devices are very useful to glider pilots as they enable the pilots to obtain maximum performance from their aircraft. They are not found in airplanes however, as airplanes rarely have to maximize their glide performance -- they have engines that eliminate concerns over vertical motion of the airmass.... in most cases. There are situations that do require the airplane pilot to be able to maximize the airplane's performance while flying through a descending airmass. One of these is an encounter with mountain wave, and these are not all that rare when flying in mountainous areas, particularly during winter months. Mountain wave is an atmospheric phenomenon in which an obstruction (typically a mountain ridge) excites air currents into a standing wave pattern of up and down vertical flow. It can be visualized as ripples downstream of a stone in water. Waves typically begin to form when winds across mountain peaks exceed 25 knots, with the wind direction being within 30 degrees of perpendicular to the line of the mountain ridge. The vertical rates of flows in mountain waves have been reported to 8,000 feet per minute, with rates of several thousand feet per minute being common. These rates greatly exceed the climb performance of most light airplanes, particularly at the high elevations at which they are encountered. In the western United States, wave is generally encountered in mountainous areas at altitudes above 7,000 feet. Climb performance in still air at these altitudes is on the order of 300 to 500 feet per minute. Most airplane pilots react to downdrafts by attempting to climb. This works as long as the intensity of the downdraft is not too severe. If the downdraft is moderate, the airplane may be able to maintain altitude. Once the downdraft exceeds the airplane's climb capability it will begin to descend. At this point the airplane pilot is faced with the same problem as the glider pilot -- at what point is it beneficial to speed up in order to obtain the shallowest possible descent? The problem is that determination of that point is not simple, and most pilots don't even know how to find a reasonable approximation of the speed to fly for their airplanes under such conditions. Factor's in Determining Speed-to-Fly The starting point in determining speeds to fly for a glider is the performance polar of that glider, i.e., a plot of the descent rate of the glider in still air (no vertical currents) over its range of airspeeds. A similar plot can be made for airplanes although it will look somewhat different, as the airplane climbs under power. There are actually a continuous series of curves for airplanes as the climb performance changes with altitude. A further complication is that climb speeds and rates change with aircraft weight. Thus the curves change continuously as altitude and weight vary. In thermal soaring the aircraft polar plus airmass motion is all that's required to determine the speed to fly. Mountain wave flying adds another parameter, namely that of wind speed. In thermal flying the aircraft moves with the airmass, thus no compensation for the speed of the airmass is necessary. In wave flying, lift and sink are oriented in a standing wave and the aircraft glide must be considered relative to the ground. Thus wind speed and direction and direction of flight are all significant factors. Given the inputs of aircraft performance information, weight, temperature, altitude, heading, airspeed, and ground track and speed, a flight computer could easily determine the downdraft intensity and suggest an optimum speed (and direction) to fly to escape from the downdraft. Such computers are not available, so the pilot must use some technique to approximate the optimal solution. Several factors can be used to reduce the complexity of the problem and thus simplify in-flight calculation and decision making. . First, the conditions under which mountain waves form are known, so only the data for those conditions need be considered. These include wind speed and direction, the likely orientation of waves, and the altitude at which they will be encountered. Next, a performance polar for the airplane is needed. This presents a problem in that polars are rarely available for light airplanes. What is available is the aircraft operating handbook which usually includes two points on the polar. These are the climb and cruise performance at a given weight and altitude. Every pilot should know the approximate performance level of his or her aircraft, and these numbers can be verified empirically during climb and flight outside of mountain wave conditions. The climb and cruise data are not sufficient to find the optimum speed to fly given a downdraft of arbitrary intensity. However it is a simple matter to determine which of these speeds produces better performance for downdrafts of various strengths. If the downdraft intensity is expressed as a ratio to the expected climb performance of the airplane, then given a set of wind conditions, we can determine when it is better to fly at best rate of climb speed (Vy) or to speed up and fly at cruise speed. The attached downdraft performance study presents data for 26 different types of airplanes ranging from 100 horsepower trainers to a medium twin of 750 total horsepower. Conditions represented are for winds aloft of 30 knots (an approximate minimum for formation of mountain waves) and 60 knots (a higher value to show the trend at significantly higher wind speeds) at an altitude of 8,000 feet, which is representative of downdraft encounters that have resulted in accidents. For each of these conditions the point is calculated at which flight at Vy and cruise airspeed yield the same descent angle. This is expressed in terms of vertical speed down versus expected vertical speed up in still air conditions. For example, for a 1980 Cessna 172, in a 30 knot headwind, if the airplane is flying at Vy and is descending at a rate of 1.08 times the expected rate of climb in still air, it will descending at the same angle as it would if it were flown at cruise speed (it would be descending at a higher rate at cruise speed, but at the same angle). If the airplane is descending at a rate greater than 1.08 times the expected rate of climb, then the airplane will descend at a shallower angle when speed is increased to cruise speed. A table of numbers of this type would be very difficult to memorize. A simpler approach to utilizing this information is necessary. An examination of these data show that the point at which it is preferable to fly at cruise speed versus Vy is fairly consistent across this wide range of types. For headwinds of at least the velocity required for formation of mountain wave, the point where Vy and cruise speed yield the same results is approximately where the descent rate while flying at Vy is equal to the expected climb rate in still air. When flying downwind, the tradeoff point occurs when the descent rate is about three times the expected climb rate. We can derive from these data general rules that are very easy to use in flight. Rules of Thumb The most critical case in dealing with a mountain wave downdraft is when flying directly into the wind, as ground speed is greatly reduced thus increasing the length of time the aircraft spends in the downdraft, the altitude lost in the downdraft, the forward progress of the aircraft and hence the angle of descent. Thus if only one rule is to be remembered, it is this: If you're at Vy, and YOU ARE GOING DOWN FASTER THAN YOU SHOULD BE GOING UP, SPEED UP TO CRUISE SPEED. A refinement of this rule takes into account wind direction and velocity versus direction of flight. This results in three rules, plus an observation.... If flying into a headwind and you're at Vy, and YOU ARE GOING DOWN FASTER THAN YOU SHOULD BE GOING UP, SPEED UP TO CRUISE SPEED. If flying with a tailwind and you're at Vy, AND YOU ARE GOING DOWN THREE TIMES AS FAST AS YOU SHOULD BE GOING UP, SPEED UP TO CRUISE SPEED. THE GREATER THE HEAD WIND, THE SOONER YOU SHOULD INCREASE TO CRUISE SPEED. All else being equal, IT'S BETTER TO FLY DOWNWIND AND FAST. A pilot who primarily flies one or two airplanes could use the exact numbers shown in the attached table or calculate numbers that are closer to the actual altitudes and winds expected. The exact point at which to speed up is not critical though. It will not make much difference if the vertical rate decision point is off by a few percent. The important point is to recognize the trend and to know that increased speed is beneficial under conditions of strong downdrafts. In the case of the accident that motivated this study the speed of the headwind was nearly 60 knots, and while the airplane was flying at Vy it was descending at nearly three times its expected climb rate. In this case the descent angle would have been greatly reduced had the airplane been flown at cruise speed instead of Vy. It probably would have cleared the ridge by about the same distance above the peak as the distance below the peak that it actually impacted while flown at Vy. Copyright Steven H. Philipson, February 1993
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