Performance At A GlanceBy John Thorp, EAA 1212

I. INTRODUCTION

Airplane performance is a very nebulous study. Thisis so for a number of very solid reasons.

1. Airplanes operate in a media which is almostalways in motion in respect to the earth and which con-stantly changes its physical properties.

2. Airplane engine output is effected by the prop-erties of air.

3. Airplane performance is effected by engine per-formance, by properties of air and by the motion of airin respect to any fixed point on the earth's surface.

4. Many of the means of gauging performance areinfluenced by the properties of air.

This new series of articles will deal with airplaneperformance as it applies to small airplanes of typeswhich are likely to be built by members of the EAA.It is not intended that the methods described will bescientifically rigorous for all airplane types and becausethe scope is restricted to a specialized "breed" of air-planes, many simplifications can and will be made overtraditional theses on this subject.

Before we can begin any performance discussion,we must review the properties of air and how in turnthese properties effect airplane performance and themeans by which performance is gauged.

The air in which we fly is an ocean surroundingthe earth. Gravity attracts each particle of air out asfar as there is any air to be attracted, pulling it towardthe center of the earth. Atmospheric pressure on anypoint of the earth's surface or at any point in spaceis the actual weight of all the air, in a column of arbi-trary cross section that exists beyond that point. Whenthe barometer reads 29.92" Hg at a given point, a columnof air one foot square rising to infinity above that pointwill weigh 2116.4 pounds. The pressure at the pointis therefore 2116.4 pounds per square foot or 14.7 poundsper square inch. Obviously the higher we go the lesswill be the weight of the air existing above our positionand the lower will be the pressure. In this country, airpressure known as barometric pressure is expressed interms of the height of a column of mercury which exertsthe same pressure on a point as does the atmosphere.We measure the height of the mercury column in inchesin this country, hence 29.92 inches of Hg has becomethe measure of standard sea level barometric pressure.

Because the air ocean is of uneven depth and con-stantly varying in depth, the pressures at various pointson the earth surface vary from day to day and hour tohour. At a point where the air ocean is shallow thepressure on the surface is low; at a spot where the depthis greater the pressure is higher so we have a tendencyof the air to flow from the high pressure area towardthe low pressure area producing wind and tending toeven up the depth of the air ocean. The air ocean isconstantly in motion and with constantly changing proper-ties. An airplane, regardless of its size, is like a chip onthe sea in respect to the magnitude of atmosphere.

When air is heated, its molecules become more ac-tive and a given weight of air will tend to occupygreater volume. Heated air is therefore less dense. Whenair is heated, cooler, heavier air will tend to move inand displace it upward. Over a warm spot on the earth'ssurface, we have rising columns of air. As the air rises

into regions of lesser pressure, it will expand whichccols the air hence we have rising and falling columnsof air whenever we have uneven heating or cooling ofthe earth's surface and we have the concept of verticalcurrents in the atmosphere in addition to horizontal.

Air has viscosity which, like a fluid tends to clingto any body immersed in it. Lift and drag are results ofthis phenomenon.

Since the properties of air are so variable, it wasessential that someone should establish a standard set ofproperties to which all airplane performance could be re-lated, knowing actual properties at the time the per-formance was measured, thereby establishing standardperformance. This was done by the National AdvisoryCommittee for Aeronautaics in 1925 and the results werepublished as NACA Technical Report No. 218. Thesedata are still in use as standard and will be used in thisseries of articles wherever properties of air are referredto.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 interms of barometric pressure. That atmospheric condi-tions are seldom standard has just been established. Whatis now needed is to establish the magnitude of day today deviations from standard and their influences uponflight.

If the barometric pressure scale of an aneroid altim-eter is properly set to indicate a known field heightwhile you are on the ground or if set in the air to aradioed altimeter setting, the indicated Pressure Alti-tude is sufficiently correct to be used for all trafficproblems and terrain clearance. However, the altitudeeffects upon performance may be something entirelydifferent than would be expected under the indicatedconditions. All "airplane drivers" have been plagued atone time or another by the apparent perversity of atmos-phere.

Nowhere on the airplane side of the performanceequation does atmospheric pressure as such appear; yetpressure is what the Altimeter indicates. All aerodynamicforces in flight (lift, drag, etc.), are directly proportionalto Mass Density of the air (symbol />) and performance iscorrected to Standard from Observed by employing func-

ptions of the Density Ratio />„ (symbol a). "Density is theThing".

At any Pressure Altitude the density of the air isa function of temperature. At any altitude where thetemperature is Standard the Density Altitude and Pres-sure Altitude are one and the same. If the temperatureis higher than Standard the Density Altitude will behigher than the Pressure Altitude (indicated altitude)and vice-versa.

Standard Air at sea level has long been defined asfollows:

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• i i u 1000 feet).

SPORT AVIATION 27

Standard Temperatures based upon the above rela-tionships are as follows:

Alt. Ft.

—4000300020001000Sea Level1000200030004000500060007000800090001000011000120001300014000150001600017000180001900020000

Temp. Deg. F.

73.369.766.162.659.055.451.948.344.741.237.634.030.526.923.319.816.212.69.15.51.9

—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 bydetermining the number of degrees by which it deviatesfrom Standard for that altitude, the appropriate DensityAltitude increment from the following table may be ap-plied. The Pressure Altitude is that shown on the al-timeter scale when the barometic scale is set at 29.92" Hg.

INCREMENT—PRESSURE ALTITUDE TODENSITY ALTITUDE

TemperatureDeviation

From StandardDegrees Fahr.

05

10152025303540455055606570758085

Above StandardTemperature

Add Feet

0327652974

12941612192722372545285031503448374340354325461449025187

Below StandardTemperature

Subtract Feet

0332667

100713501698205224122777314735233905429546955105

To illustrate the theme of this section, the followingexamples are cited.

After taking off from sea level field (Bar. 29.92" Hg.)an airplane is set for normal cruising conditions one

thousand feet above the point of take-off. If conditionsare Standard the O.A.T. will read 55.4T. and the Al-timeter will read 1000 feet. The Density Altitude willalso be 1000 feet. If the airplane cruises at 100 M/H un-der these conditions the air speed indicator (A.S.I.) willbe showing approx. 99 M/H. The pilot, knowing that a1 Vi percent correction for altitude is in order, will notbe concerned.

However, if instead of 55° the O.A.T. reads 85°under the above conditions, a 1927 foot increment wouldneed to be added to the indicated altitude to establishthe Density Altitude at which the airplane is flying.The Density Altitude is therefore approximately 3000feet or three times the Indicated Pressure Altitude. Un-der these conditions the A.S.I, would be reading about96 M/H and the pilot might be wondering what hadhappened to the advertised 100 M/H cruising speed. Ifhe added a 4V2 percent correction for Density Altitudeto the A.S.I, reading instead of the l\'z percent PressureAltitude correction, the True Air Speed would work outto be approximately 100 M/H, just like it was supposedto be.

On the other hand, if the OAT shows 10° belowzero at 1000 feet, the temperature increment is 65° be-low Standard and the Density Altitude would be (4695—1000) or approximately 3700 feet below sea level. Underthese conditions the A.S.I, would be showing approx.106 M/H and the pilot is apt to be blissfully happy inspite of the cold.

In the South West during the summer months, it isnot uncommon to encounter 100° temperatures at someof the 7000 ft. high airports. At 7000 ft. the Standardtemperature is 34°F. The resulting 66° temperature in-crement yields an approx. 4000 foot Density Altitudeincrement, so that as far as the airplane knows, it isbeing asked to take off at an 11,000 foot altitude. It issmall wonder that under such conditions, they sometimesrefuse to leave the ground.

To properly evaluate your performance, you mustknow "how high is up".

III. HOW FAST DOES IT GO?

The first question always asked of the pilot whobrings in an airplane strange to any airport is, "Howfast does it go". Though ungrammatical this is a goodquestion for several reasons:

1. It emphasizes speed as the fundamental reasonfor flying.

2. Unconsciously, speed has become an order ofmerit to most people.

3. Very few pilots really know how fast their air-planes do go. This is because of the extreme variabilityof the airplane's operating media — air.

Fundamentally all Airspeed Indicators are PressureGauges and are calibrated to read Dynamic Pressure(symbol q) expressed in miles per hour units, "q" is di-rectly proportional to the velocity squared and to theMass Density of the air (symbol />). "/>" varies with alti-tude and temperature. For any Density Altitude, theDensity Ratio (symbol a) is U)The speed indicated on the dial of an Airspeed Indicatoris therefore proportional to V<r and True air speed is in-dicated air speed times / i

v —Values of /T~for Density Altitudes up to 20,000 feet

v —are given in the following table:

28 JANUARY 1961

Density AltitudeFeet

—4000300020001000

Sea Level1000200030004000500060007000800090001000011000120001300014000150001600017000180001900020000

Airspeed CorrectionFactor = / 1

V a

0.9440.9570.9710.9861.0001.0151.0301.0451.0611.0771.0941.1111.1281.1461.1641.1821.2011.2211.2401.2611.2821.3031.3251.3471.370

To obtain the True air speed, the pilot has only todetermine the Density Alttiude at which he is flying(See "How High Is Up") and multiply the Indicated airspeed by the Airspeed Correction Factor for the ap-proprite Density Altitude (see table).

At this point it may be well to call attention to therelationship which exist between the Airspeed Indicatorreading at Altitude and the stalling and climbing speedsof an airplane. Lift is directly proportional to the velocitysquared and to p. The True stalling speed at altitude istherefore proportional to /Tand the unaccelerated stallv —will occur at the same Indicated air speed regardless ofaltitude. A somewhat similar relationship exists betweenthe speed for best climb and the Airspeed reading. Thespeed for best climb for some airplanes will actually beat a slightly lower Indicated air speed at altitude thanat sea level. This points out the fallacy in the practice ofclimbing or gliding at higher indicated air speeds on ahot day or at high altitudes than would be employed ona Standard day at sea level.

Airspeed indicators which compensates automaticallyfor Density altitude effects have been developed and areavailable. They (True air speed indicators) are not ingeneral use, however, because of cost and complexityand because they should not be used except in conjunc-tion with a standard airspeed indicator. It would bevery confusing to the pilot to be forced to determine asafe approach speed based upon Density altitude beforeeach landing. Also, safe maximum speed limits are usual-ly based upon Dynamic pressure and at this end of thespeed range the standard airspeed indicator also has theadvantage and should therefore be included in the flightgroup.

Aside from the fundamental limitations on the ac-curacy of the readings of an Airspeed indicator, justdiscussed, there are many detail possibilities for error.Some of these creep into the picture in spite of the bestintentions. Some are accepted as a concession to lowcost while others are introduced deliberately.

At best, it is difficult to find a suitable location forthe Airspeed sampling unit, usually a Pilot-Static head.Air at some distance ahead of a moving body anticipatedits proximity and starts to move out of the way causinga reduction in Dynamic pressure. Air along the surfaceof a body tends to cling to the body and move along withit causing a loss in Dynamic pressure which becomesgreater with distance along the body. Because of themechanics of lift, velocities above an airplane tend tobe on the high side with a corresponding increase inDynamic pressure. Below an airplane the velocities aresomewhat retarded with a corresponding loss in Dy-namic pressure. The foregoing only generally states theproblem of finding a suitable location for the Pitot-Statichead. Bumps which increase local velocity and tend toreduce Static pressure, bad fairing which tends to intro-duce flow discontinuities, etc., all add to the problem.Actually it is usually more difficult to find a region oftrue Static pressure than to find a region of correct Dy-namic pressure. The so-called "flush" static arrange-ment frequently seen these days is premised on the factthat the Dynamic pressure taken almost anyplace on anairplane will be a large percentage of free stream "q",while the Static pressure may vary considerably. By find-ing a suitable static vent location, not necessarily in asuitable Dynamic pressure region, the designer, by separ-ating the Static and Dynamic pressure lines, has consid-erable more latitude in locating the Pilot than he wouldhave in locating a Pitot-Slatic head. As if the pressureproblem is not difficull enough, conditions al a givenlocalion on an airplane oflen lend lo change dispropor-tionately with changes in attitude so that it is usuallynot possible to build a correction factor into the instru-menl ilself.

The FAA requires lhat an Airspeed indicator instal-lation be accurate within plus or minus 3 percenl or5 M/H, whichever is Ihe grealer. Slrange as it may seemthese close limits can be met and are mel before anairplane is cerlificaled. The wide variely of Pilol-Slaticinstallations commonly seen on various makes and modelsis eloquent evidence of the difficulties which have hadto be surmounted.

Ironically enough, after going through all the painsof developing and proving a Pitol-Slalic installationwhich will meet FAA requiremenls, airplanes seldommainlain prololype Airspeed accuracy. Inexpensive Air-speed indicalors, subject lo some plus or minus loler-ance, always seem lo lesl oul on Ihe high side of perfectcalibration. While wilhin FAA limils, airplane manufac-turers are not inclined to accept instruments which readlow. Large rivet heads and even deflectors are placedjust ahead of flush Stalic openings resulling in lowpressure on Ihe slalic side of Ihe inslrumenl making ilread high. Generous leaks in Ihe slalic line are oflenprovided in Ihe cabin area (usually an area of low pres-sure) giving high readings. Al one time stalic lineswere eliminated altogether on many low priced air-planes. Large washers placed just ahead of the staticholes of a Pitol-Slalic head, deliberale misalignmenl ofIhe slalic elemenl, elc., are jusl a few of Ihe ways lhalAispeed indicalors are made lo exaggerale Iheir read-ings. Because Ihe cabin pressure of high wing airplanesis apl to be slightly positive at stall and become quilelow al high speed, elimination of the vent line willcause the Airspeed to read low at low speed and high alhigh speed. Some enlerprising people have found wayslo provide the same sort of an indicaled speed rangeincrease for low wing airplanes. A Pilot-Stalic headplaced below a wing will cause a slighlly low reading athigh speed and a very low reading al low speed. By

SPORT AVIATIION 29

placing a generous washer ahead of the vent holes ofthe Pitol-Static head the discrepancy can be shifted sothat the Airspeed will read high at high speed and lowat low speed which seems to be the way that "airplanedrivers" like them to be.

Most of the methods employed by Airplane Peopleto "kid" themselves as to how fast their airplanes go areobvious upon inspections. A simple check on the staticline situation is to open the cabin door slightly in flight.If the static line is open the Airspeed will show a suddenupward fluctuation as will the sensitive altimeter, ifpresent.

By flying along side several onetime popular per-sonal airplanes in an airplane which has a very carefullycalibrated Airspeed, the following results were recorded.

Airplone With Inexpensive" PopularCalibrated A.S.I. 2-Plac« 2-Place

Advanced Popular2-Place 4-plae«

60 66

90 10560 55

107 11870

10570

100

55

10865

110

*No static line installed

The possible justification for "hopping up" Airspeedslies in the fact that airplanes "are almost always flown at

an altitude higher than sea level". Also, temperatures arealmost always higher than Standard when private pilotsare venturing into the "wild blue yonder", so that a plusDensity Altitude correction is almost always in order. Ifthe manufacturer assumes that "Airplane Drivers" fre-quently don't know that a correction is in order, andeven when they do know, seldom apply it; then he mayreason that a stepped up Airspeed may, on the average,come closer to telling the pilot how fast he is going thanwould be the case with an honest Airspeed.

It is indeed a wise pilot who, by reading his Airspeed,knows "How Fast It Does Go".

IV. DENSITY ALTITUDE—TRUE AIRSPEED CHART

Data given in tables in Sections II and III can beplotted in the form of a Density Altitude—True Airspeedchart. This chart in effect is a computer in which theonly moving element is your eye ball.

To use this chart to determine your density altitudeand true airspeed:

1. Set the barometric scale of altimeter so that itreads 29.92.

2. Observe pressure altitude (read altimeter).3. Read outside air temperature.4. Density altitude is found at the intersection of

pressure altitude line and temperature line. In exampleO.A.T. is 83° F. Pressure altitude is 5,000 ft. Densityaltitude is 7,700 ft..

5. True airspeed is found at the intersection ofindicated air speed line and density altitude line. In ex-ample, the I.A.S. is 105 M/H at a density altitude of7,700 ft. True air speed (T.A.S.) is 118 M/H.

DENSITY ALTITUDE -:- TRUE AIRSPEEDSET ALTIMETER BAKOMETRIC SCALE 29.92

TEMPERATURE, F. AIR SPEcD. MILES PER HOURf94t

30 JANUARY 1961