Performance At A Glance By John Thorp, EAA 1212 I.

INTRODUCTION

Airplane performance is a very nebulous study. This is so for a number of very solid reasons. 1. Airplanes operate in a media which is almost always in motion in respect to the earth and which constantly changes its physical properties. 2. Airplane engine output is effected by the properties of air. 3. Airplane performance is effected by engine performance, by properties of air and by the motion of air in respect to any fixed point on the earth's surface. 4. Many of the means of gauging performance are influenced by the properties of air. This new series of articles will deal with airplane performance as it applies to small airplanes of types which are likely to be built by members of the EAA. It is not intended that the methods described will be scientifically rigorous for all airplane types and because

the scope is restricted to a specialized "breed" of airplanes, many simplifications can and will be made over traditional theses on this subject. Before we can begin any performance discussion, we must review the properties of air and how in turn these properties effect airplane performance and the means by which performance is gauged. The air in which we fly is an ocean surrounding the earth. Gravity attracts each particle of air out as far as there is any air to be attracted, pulling it toward the center of the earth. Atmospheric pressure on any point of the earth's surface or at any point in space is the actual weight of all the air, in a column of arbitrary cross section that exists beyond that point. When the barometer reads 29.92" Hg at a given point, a column of air one foot square rising to infinity above that point will weigh 2116.4 pounds. The pressure at the point is therefore 2116.4 pounds per square foot or 14.7 pounds per square inch. Obviously the higher we go the less will be the weight of the air existing above our position and the lower will be the pressure. In this country, air pressure known as barometric pressure is expressed in terms of the height of a column of mercury which exerts the same pressure on a point as does the atmosphere. We measure the height of the mercury column in inches in this country, hence 29.92 inches of Hg has become the measure of standard sea level barometric pressure. Because the air ocean is of uneven depth and constantly varying in depth, the pressures at various points on the earth surface vary from day to day and hour to hour. At a point where the air ocean is shallow the pressure on the surface is low; at a spot where the depth is greater the pressure is higher so we have a tendency of the air to flow from the high pressure area toward the low pressure area producing wind and tending to even up the depth of the air ocean. The air ocean is constantly in motion and with constantly changing properties. An airplane, regardless of its size, is like a chip on the sea in respect to the magnitude of atmosphere. When air is heated, its molecules become more active and a given weight of air will tend to occupy greater volume. Heated air is therefore less dense. When air is heated, cooler, heavier air will tend to move in and displace it upward. Over a warm spot on the earth's surface, we have rising columns of air. As the air rises

into regions of lesser pressure, it will expand which ccols the air hence we have rising and falling columns of air whenever we have uneven heating or cooling of the earth's surface and we have the concept of vertical currents in the atmosphere in addition to horizontal. Air has viscosity which, like a fluid tends to cling to any body immersed in it. Lift and drag are results of this phenomenon. Since the properties of air are so variable, it was

essential that someone should establish a standard set of properties to which all airplane performance could be related, knowing actual properties at the time the performance was measured, thereby establishing standard performance. This was done by the National Advisory Committee for Aeronautaics in 1925 and the results were published as NACA Technical Report No. 218. These data are still in use as standard and will be used in this series of articles wherever properties of air are referred to. II.

HOW HIGH IS UP?

Your altitude is probably "different than you think." The aneroid altimeter is a pressure gauge calibrated to indicate equivalent height in standard atmosphere in terms of barometric pressure. That atmospheric conditions are seldom standard has just been established. What is now needed is to establish the magnitude of day to day deviations from standard and their influences upon flight. If the barometric pressure scale of an aneroid altimeter is properly set to indicate a known field height while you are on the ground or if set in the air to a radioed altimeter setting, the indicated Pressure Altitude is sufficiently correct to be used for all traffic problems and terrain clearance. However, the altitude effects upon performance may be something entirely different than would be expected under the indicated conditions. All "airplane drivers" have been plagued at one time or another by the apparent perversity of atmosphere. Nowhere on the airplane side of the performance equation does atmospheric pressure as such appear; yet pressure is what the Altimeter indicates. All aerodynamic forces in flight (lift, drag, etc.), are directly proportional to Mass Density of the air (symbol />) and performance is corrected to Standard from Observed by employing funcp

tions of the Density Ratio />„ (symbol a). "Density is the Thing". At any Pressure Altitude the density of the air is a function of temperature. At any altitude where the temperature is Standard the Density Altitude and Pressure Altitude are one and the same. If the temperature is higher than Standard the Density Altitude will be higher than the Pressure Altitude (indicated altitude) and vice-versa. Standard Air at sea level has long been defined as follows: Barometric Pressure, Po = 29.92" Hg , . Fahrenheit Temperature, to = 59 Deg. Temperature Variation with Altitude (lapse rate) ,. i is established as 0.003566°F per foot (3.6°F. per • iiu 1000 feet). SPORT

AVIATION

27

Standard Temperatures based upon the above relationships are as follows:

Alt. Ft.

Temp. Deg. F.

—4000 3000 2000 1000 Sea Level 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000

73.3 69.7 66.1 62.6 59.0 55.4 51.9 48.3 44.7 41.2 37.6 34.0 30.5 26.9 23.3 19.8 16.2 12.6 9.1 5.5 1.9 —1.6 —5.2 —8.8 —12.3

By observing the Outside Air Temperature (O.A.T.) at the Pressure Altitude at which you are flying and by determining the number of degrees by which it deviates from Standard for that altitude, the appropriate Density Altitude increment from the following table may be applied. The Pressure Altitude is that shown on the altimeter scale when the barometic scale is set at 29.92" Hg. INCREMENT—PRESSURE ALTITUDE TO

DENSITY ALTITUDE Temperature Above Standard Deviation Temperature From Standard

Degrees Fahr.

Add Feet

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

327 652 974 1294 1612 1927 2237 2545 2850 3150 3448 3743 4035 4325 4614 4902 5187

0

Below Standard Temperature Subtract Feet

0 332 667 1007 1350 1698 2052 2412 2777 3147 3523 3905 4295 4695 5105

To illustrate the theme of this section, the following examples are cited. After taking off from sea level field (Bar. 29.92" Hg.) an airplane is set for normal cruising conditions one 28

JANUARY

1961

thousand feet above the point of take-off. If conditions are Standard the O.A.T. will read 55.4T. and the Altimeter will read 1000 feet. The Density Altitude will also be 1000 feet. If the airplane cruises at 100 M/H under these conditions the air speed indicator (A.S.I.) will be showing approx. 99 M/H. The pilot, knowing that a 1 Vi percent correction for altitude is in order, will not be concerned. However, if instead of 55° the O.A.T. reads 85° under the above conditions, a 1927 foot increment would need to be added to the indicated altitude to establish the Density Altitude at which the airplane is flying. The Density Altitude is therefore approximately 3000 feet or three times the Indicated Pressure Altitude. Under these conditions the A.S.I, would be reading about 96 M/H and the pilot might be wondering what had happened to the advertised 100 M/H cruising speed. If he added a 4V 2 percent correction for Density Altitude to the A.S.I, reading instead of the l\'z percent Pressure Altitude correction, the True Air Speed would work out to be approximately 100 M/H, just like it was supposed to be. On the other hand, if the OAT shows 10° below zero at 1000 feet, the temperature increment is 65° below Standard and the Density Altitude would be (4695— 1000) or approximately 3700 feet below sea level. Under these conditions the A.S.I, would be showing approx. 106 M/H and the pilot is apt to be blissfully happy in spite of the cold. In the South West during the summer months, it is not uncommon to encounter 100° temperatures at some of the 7000 ft. high airports. At 7000 ft. the Standard temperature is 34°F. The resulting 66° temperature increment yields an approx. 4000 foot Density Altitude increment, so that as far as the airplane knows, it is being asked to take off at an 11,000 foot altitude. It is small wonder that under such conditions, they sometimes refuse to leave the ground. To properly evaluate your performance, you must know "how high is up". III.

HOW FAST DOES IT GO?

The first question always asked of the pilot who brings in an airplane strange to any airport is, "How fast does it go". Though ungrammatical this is a good question for several reasons: 1. It emphasizes speed as the fundamental reason for flying. 2. Unconsciously, speed has become an order of merit to most people. 3. Very few pilots really know how fast their airplanes do go. This is because of the extreme variability of the airplane's operating media — air. Fundamentally all Airspeed Indicators are Pressure Gauges and are calibrated to read Dynamic Pressure (symbol q) expressed in miles per hour units, "q" is directly proportional to the velocity squared and to the Mass Density of the air (symbol />). "/>" varies with altitude and temperature. For any Density Altitude, the Density Ratio (symbol a) is

U)

The speed indicated on the dial of an Airspeed Indicator is therefore proportional to V