From day one through a Cessna 152 or a Piper Cherokee, we pilots are conscious that we just have a limited amount of time before our powered trip aeroroom machines come to be gliders. Several of the aircraft I"ve flvery own are not landable without petroleum products turning the engines and many of the others are less than elegant when trying to do so. Our job, then, is to have the ability to predict the airplane"s range in regards to distance or time.

You are watching: Which maximum range factor decreases as weight decreases?

A caveat: aerodynamic considerations for propeller thrust airplanes are various than for turbojets. Tbelow are additionally variations between turbine and also reciprocating engines. Most textpublications take into consideration propeller pushed airplanes as one category and also turbojets as one more. You might argue that a contemporary turbofan engine is a hybrid. Because many of my formal education on the topic originates from the people of turbojets, though the majority of of my flying has actually been with turbofans, I will consider them cshed enough and narrow my aerodynamic discussion to the people of turbojets.


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Photo: E-4B Air Refueled by KC-135A, from USAF Photo


About the photo below, I"ve flvery own both aircraft. The KC-135A"s cold battle mission wregarding offload eexceptionally drop of fuel it had actually to a B-52 bomber. It was a flyable glider however certainly not an excellent one. I also flew the E-4B, a Boeing 747-200. It brought 303,000 lbs of fuel, burned 25,000 lbs an hour, however could onpack eexceptionally drop of fuel that tanker had to market. We used to say our endurance was 72 hrs, restricted only by the capacity of the engine oil reserves. We later uncovered out our limiting factor was the capacity of the lavatories.

Everypoint right here is from the recommendations shown below, with a couple of comments in an alternative shade.


Last revision:
Range Performance

Endurance versus Range

Maximum Endurance
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Figure: Drag or thrust forced versus velocity, propeller-thrust aircraft, from Eddie"s notes.


All aircraft should create thrust to conquer the drag of the aircraft. In turbojets and also in other thrust-producing aircraft, this thrust is developed straight from the engine. In aircraft that have propellers (or rotors), the engine does not produce thrust straight. These aircraft are referred to as power producers because the power turns the propeller. The propeller, subsequently, establishes an aerodynamic force as soon as it is turned via the air; this force is thrust. Fuel consumption of power-developing aircraft is approximately proportional to the power developed, quite than the thrust created. Range and endurance performance are features of fuel usage, and also so the power forced to fly the aircraft is of prime prominence.

By plotting the power forced to keep secure, unaccelerated trip versus the resulting velocity, you deserve to gain a visual representation of what it takes to save the aircraft flying for any given weight, altitude, and also configuration. Since the aircraft is in a secure trip problem, drag equals the thrust, which is analogous to the power.

Maximum endurance occurs once you have the biggest amount of flying time (T) for the least amount of fuel (F). Sassist another means, T/F is at a maximum. As have the right to be viewed below under Specific Endurance, the reciprocal of the fuel flow is your endurance and you gain the ideal endurance at the low suggest of the curve.

The suggest wbelow the proportion of lift-to-drag is at its greatest is dubbed L/DMAX. In a propeller-thrust aircraft, this suggest occurs at a speed somewhat faster than the low allude of the curve. (More on how to uncover the allude a small later.) For now the essential takeamethod is this: maximum endurance in a propeller-thrust aircraft occurs at a speed listed below L/DMAX.


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Figure: Drag or thrust forced versus velocity, turbojet aircraft, from Eddie"s notes.


Unfavor a propeller-thrust aircraft, a turbojet produces thrust directly from the engines. The absence of a propeller profoundly alters the way a turbojet flies. The drag or thrust required versus velocity graph looks different as a result. A turbojet generally has actually the pronounced "u" shape because the induced drag is exceptionally high at sluggish speeds (it takes a high angle of attack) and also aacquire at high speeds (the parasite drag becomes restrictive).

The point where the total drag is at a minimum will likewise be the suggest wbelow the lift-to-drag ratio will certainly be at a maximum. For a turbojet, this point is well-known as L/DMAX.

The minimum drag point still represents where the propeller-propelled aircraft obtains maximum endurance because it is still the lowest allude of the curve. L/DMAX is somewhat faster.

Maximum Range
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Figure: Fuel circulation forced versus velocity, propeller-thrust aircraft, from Eddie"s notes.


Maximum array occurs when you get the greatest distance (D) for a provided amount of fuel (F). The specific variety is equal to (D/F), which have the right to likewise be created (nm/lbs. of fuel). If you divide each side of this equation by 1 hour, you obtain (nm/hr) / (lbs/hr) and also that is the exact same as (V/FF). Specific variety is maximized at (V/FF)MAX, or (FF/V)MIN.

(FF/V)MIN have the right to be discovered through trigonomeattempt to be the tangent of the fuel circulation separated by the velocity:

tanθ= FF V

Graphically, drawing a line from the origin of the chart to a allude tangent to the curve will define a triangle through the FF and V as legs.

This suggest constantly describes maximum variety. In a propeller-propelled aircraft, it also explains L/DMAX.

Some aeronautical textpublications deserve to be misleading on the subject of array versus endurance bereason the entire aviation civilization adjusted through the jet engine. Prior to considering turbojets, many aeronautical texts thought about range and endurance to be the same:

Examination . . . reveals that to achieve maximum array, flight have to be carried out at maximum L/D.

In 1951, once this was composed, this was practically constantly true. It remains true for a traditional reciprocating engine through a propeller. With a jet engine, but, flying at L/DMAX gets you maximum endurance. If you desire maximum array, you will certainly should fly quicker. that"s why were are here . . .


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Figure: Fuel circulation required versus velocity, turbojet aircraft, from Eddie"s notes.


In a turbojet, maximum range also occurs at the tangent point defined for propeller-thrust aircraft, yet this allude will not be at L/DMAX, it will be at a greater speed.

Specific Range

The problem of effective array operation of an plane appears of two basic creates in flying operations: (1) to extract the maximum flying distance from a offered fuel load or (2) to fly a mentioned distance with minimum expenditure of fuel. An noticeable prevalent denominator for each of these operating difficulties is the "certain range," nautical miles of flying distance per lb. of fuel.

The particular array deserve to be characterized by the complying with relationship:

particular range= nautical miles lbs. of fuel

or,

certain range= nautical miles/hr. lbs. of fuel/hr.

hence,

specific range= velocity, knots fuel circulation, lbs. per hr.

If maximum certain range is desired, the trip problem should administer a maximum of velocity/fuel circulation. This particular suggest would be situated by drawing a right line from the origin tangent to the curve of fuel flow versus velocity.

Specific Endurance

The general item of range need to be plainly distinguished from the item of endurance. The item of selection involves consideration of flying distance while endurance requires consideration of flying time. Thus, it is proper to specify a separate term, "certain endurance."

certain endurance= trip hours lbs. of fuel

or,

particular endurance= trip hours/hr. lbs. of fuel/hr.

then,

specific endurance= 1 fuel circulation, lbs. per hr.

By this definition, the certain endurance is ssuggest the reciprocal of the fuel flow. Thus if maximum endurance is desired, the trip condition have to carry out a minimum of fuel flow. This suggest is conveniently appreciated as the lowest suggest of the curve of fuel flow versus velocity. Typically, in subsonic performance, the speed at which maximum endurance is obtained is approximately 75 percent of the speed for maximum variety.

If you are holding at maximum endurance and are released to your location, what rate do you fly to usage the least amount of fuel? That would certainly be the speed for maximum selection. If VME = 0.75 VMR, then the inverse of 0.75 is 1.33. Restated: maximum range is generally a third higher than maximum endurance. (In theory, of course.)

Range Performance

General
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Figure: Range performance, general, from ATCM 51-3, figure 2.25.


In the situation of a turbojet aircraft, the fuel circulation is determined mostly by the thrust rather than power.

For a discussion on the distinctions of what drives us (between turbojet and also a propeller pushed aircraft), see: Thrust vs. Power.

Therefore, the fuel circulation might be the majority of directly related to the thrust compelled to keep the aircraft in stable, level flight. This fact enables research of the turbojet powered plane by analysis of the curves of thrust compelled versus velocity. illustrates a typical curve of thrust compelled versus velocity which would certainly be (somewhat) analogous to the variation of fuel circulation versus velocity. Maximum endurance condition would certainly be obtained at (L/D)MAX since this would incur the lowest fuel circulation to save the airplane in secure, level flight. Maximum range problem would occur wright here the propercentage in between the velocity and also thrust compelled is greatest and also this suggest is situated by drawing a directly line from the beginning to the curve.

The maximum selection is derived at the aerodynamic problem which produces a maximum proportion between the square root of the lift coeffective (CL) and the drag coreliable (CD), or (√CL/CD)MAX. In subsonic performance, (√CL/CD)MAX occurs at a specific value angle of attack and lift coreliable and is unimpacted by weight or altitude (within compressibility limits). At this certain aerodynamic condition, induced drag is about 25 percent of full drag so the turbojet plane designed for long range does not have the strong preference for high element ratio plancreate like the propeller airplane. On the various other hand also, since around 75 percent of complete drag is parasite drag, the turbojet airplane designed specifically for lengthy rage has the distinct need for good aerodynamic cleanness.

Effect of Gross Weight
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Figure: Range performance, weight, from ATCM 51-3, number 2.25.


The flight problem of (√CL/CD)MAX is achieved at one worth of lift coefficient for a provided aircraft in subsonic trip. Hence, a variation of gross weight will certainly change the worths of airspeed, thrust compelled, and particular variety acquired at (√CL/CD)MAX. If a given configuration is operated at constant altitude and lift coeffective the adhering to partnership will apply:

V 2 V 1 = W 2 W 1 T r2 T r1 = W 2 W 1 SR 2 SR 1 = W 2 W 1 (consistent altitude)

where

problem (1) applies to some known condition of velocity, thrust compelled, and specific selection for (√CL/CD)MAX at some standard weight, W1

condition (2) uses to some new values of velocity, thrust required, and also particular array for (√CL/CD)MAX at some standard weight, W2

and

V = velocity, knots

W = gross weight, lbs.

Tr = thrust forced, lbs.

SR = particular range, nmi/lb.

Hence, a 10 percent boost in gross weight would certainly create:

a 5 percent increase in velocity

a 10 percent rise in thrust required

a 5 percent decrease in particular range

as soon as trip is preserved at the optimum conditions of (√CL/CD)MAX at some basic weight, W2. Due to the fact that most jet airplanes have actually a fuel weight which is a huge component of the gross weight, cruise manage actions will be necessary to account for the alters in optimum airspeeds and power settings as fuel is consumed.

All this suggests to the pilot is this: if you desire to keep maximum selection while burning off fuel, your airrate is going to need to come earlier. That consequently will certainly decrease your forced thrust establishing while enhancing your certain selection. Alternatively, you deserve to take into consideration climbing.

Effect of Altitude
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Figure: Range performance, altitude, from ATCM 51-3, number 2.25.


The result of altitude on the selection of the turbojet airplane is of great prestige because no various other single item can cause such huge variations of specific array. If a given configuration of aircraft is operated at continuous gross weight and the lift coeffective for (√CL/CD)MAX a readjust in altitude will develop the complying with relationships:

where

problem (1) uses to some known condition of velocity, thrust compelled, and particular range for (√CL/CD)MAX at some original, basic altitude.

problem (2) uses to some brand-new values of velocity, thrust required, and specific variety for (√CL/CD)MAX at some different altitude.

and

V = velocity, knots, TAS

Tr = thrust required, lbs.

SR = specific range, nmi/lb.

σ = altitude thickness proportion (sigma)

Thus, if trip is conducted at 40,000 ft. (σ = 0.246), the plane will have:

a 102 percent higher velocity

the same thrust required

a 102 percent higher certain selection (even when the helpful impacts of altitude on engine performance are neglected)

than as soon as operating at sea level.

Notice that the entire thrust required curve shifts up and to the best through a boost in altitude. An boost in altitude calls for more thrust and also velocity.

An rise in altitude will certainly boost powerplant performance in 2 respects. First, an increase in altitude as soon as below the tropopausage will certainly provide reduced inlet air temperatures which minimize the specific fuel intake. Of course, over the tropopausage the certain fuel usage has a tendency to boost. At low altitude, the engine RPM vital to create the forced thrust is low and, primarily, well listed below the normal rated value. Therefore a 2nd benefit of altitude on engine performance is because of the increased RPM compelled to furnish cruise thrust. An boost in engine speed to the normal rated worth will reduce the specific fuel consumption.

The boost in certain range via altitude of the turbojet aircraft can be attributed to these 3 factors:

An boost in altitude will rise the proportion of (V/Tr) and also carry out a better TAS for the very same Tr. An rise in altitude in the troposphere will certainly produce reduced inlet air temperature which reduces the particular fuel intake. An boost in altitude requires enhanced engine RPM to carry out cruise thrust and also the particular fuel consumption reduces as normal rated RPM is approached.

From the previous evaluation, it is obvious that the cruise altitude of the turbojet have to be as high as possible within compressibility or thrust limits. Generally, the optimum altitude to begin cruise is the highest possible altitude at which the maximum consistent thrust deserve to provide the optimum aerodynamic problems.

Two points:

Many jet engines are more reliable at high RPM"s, you will certainly get better selection operating near the engine"s RPM boundaries. Planning on operating at the upper limit of the airplane"s cruise capcapacity poses a hazard if the external air temperature rises. You may find the plane at a higher altitude than it is capable of sustaining. Effect of Wind
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Figure: Effect of wind on range, from ATCM 51-3, figure 2.26.


The result of wind on selection is of considerable prestige in flying operations. Of course, a headwind will certainly always alleviate variety and also a tailwind will always increase selection. The selection of a cruise altitude with the many favorable (or leastern unfavorable) winds is a relatively straightforward issue for the situation of the propeller powered plane. Due to the fact that the selection of the propeller powered airplane is fairly unaffected by altitude, the altitude through the a lot of favorable winds is selected for range. However before, the selection of the turbojet plane is significantly affected by altitude so selection of an optimum altitude will certainly involve considering the wind profile via the variation of variety through altitude. Due to the fact that the turbojet selection increases significantly via altitude, the turbojet can tolerate less favorable (or even more unfavorable) winds via raised altitude.

In some situations, huge values of wind might reason a far-ranging readjust in cruise velocity to preserve maximum ground nautical miles per lb. of fuel. As a severe condition, take into consideration an airplane flying into a headwind which equals the cruise velocity. In this situation, any kind of increase in velocity would improve selection.

The procedure of employing different cruise velocities to account for the impacts of wind is essential just at excessive values of wind velocity. It is essential to take into consideration the adjust in optimum cruise airspeed as soon as the wind velocities exceed 25 percent of the zero wind cruise velocity.

The impact of winds on high rate aircraft often tends to be overproclaimed. In reality, at many wind speeds adjusting aircraft speed deserve to be detrimental. I"ve looked at this for a range of aircraft. Even for those aircraft wbelow a marginal advantage is viewed under some problems, the advantage disshows up for others. My advice, do not bother adjusting without doing the math initially. Here is some anecdotal evidence:

CL604

CL604 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 33,000", 36,000 lbs
Max Range 0.63 0 366.6 366.6 0.232 1580.0 500 1+22 2155
Max Range 0.63 100 366.6 266.6 0.232 1580.0 500 1+53 2964
Faster 0.66 100 384.0 284.0 0.232 1655.3 500 1+46 2914 Speeding up in headwind helps, marginally
CL604 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 33,000", 36,000 lbs
Max Range 0.63 0 366.6 366.6 0.232 1580.0 500 1+22 2155
Slower 0.6 -100 349.1 449.1 0.23 1517.9 500 1+07 1690 Slowing down in tailwind helps, marginally

DA2000

DA2000 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 35,000", 36,000 lbs
Mid Range 0.8 0 455.0 455.0 0.2304 1974.8 500 1+06 2170
Mid Range 0.8 100 455.0 355.0 0.2304 1974.8 500 1+25 2781
Faster 0.84 100 476.0 376.0 0.2042 2331.0 500 1+20 3100 Speeding up in headwind does not help
DA2000 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 35,000", 36,000 lbs
Mid Range 0.8 0 455.0 455.0 0.2304 1974.8 500 1+06 2170
Mid Range 0.8 -100 455.0 555.0 0.2304 1974.8 500 0+54 1779
Slower 0.77 -100 439.0 539.0 0.2361 1859.4 500 0+56 1725 Slowing down in tailwind helps, marginally

G450

G450 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 41,000", 62,000 lbs
Max Range 0.746 0 427.9 427.9 0.1679 2548.6 500 1+10 2978
Max Range 0.746 100 427.9 327.9 0.1679 2548.6 500 1+31 3886
Faster 0.778 100 446.3 346.3 0.1646 2711.2 500 1+26 3915 Speeding up in headwind does not help
G450 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 41,000", 62,000 lbs
Max Range 0.746 0 427.9 427.9 0.1679 2548.6 500 1+10 2978
Max Range 0.746 -100 427.9 527.9 0.1679 2548.6 500 0+57 2414
Slower 0.73 -100 418.7 518.7 0.1678 2495.4 500 0+58 2405 Slowing dvery own in tailwind helps, marginally

G550

G550 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 43,000", 65,000 lbs
Max Range 0.725 0 415.9 415.9 0.19 2188.7 500 1+12 2632
Max Range 0.725 100 415.9 315.9 0.19 2188.7 500 1+35 3465
Faster 0.765 100 438.8 338.8 0.1895 2315.6 500 1+29 3417 Speeding up in headwind helps, marginally
G550 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 43,000", 65,000 lbs
Max Range 0.725 0 415.9 415.9 0.19 2188.7 500 1+12 2632
Max Range 0.725 -100 415.9 515.9 0.19 2188.7 500 0+58 2121
Slower 0.705 -100 404.4 504.4 0.1895 2134.0 500 0+59 2115 Slowing down in tailwind helps, marginally

G650

G650 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 45,000", 70,000 lbs
Max Range 0.82 0 470.4 470.4 0.187 2515.3 500 1+04 2674
Max Range 0.82 100 470.4 370.4 0.187 2515.3 500 1+21 3396
Faster 0.852 100 488.7 388.7 0.1865 2620.4 500 1+17 3371 Speeding up in headwind helps marginally
G650 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 45,000", 70,000 lbs
Max Range 0.82 0 470.4 470.4 0.187 2515.3 500 1+04 2674
Max Range 0.82 -100 470.4 570.4 0.187 2515.3 500 0+53 2205
Slower 0.774 -100 444.0 544.0 0.185 2399.8 500 0+55 2206 Slowing down in tailwind does not help

PC-12

PC-12 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 15,000", 8,000 lbs
LRC 0 218.0 218.0 0.61 357.4 500 2+17 820
Max Range 50 218.0 168.0 0.61 357.4 500 2+59 1064
Faster 50 240.0 190.0 0.57 421.1 500 2+38 1108 Speeding up in headwind does not help
PC-12 Mach Wind TAS GS NM/LB LB/HR DIST ETE LBS ISA, 15,000", 8,000 lbs
LRC 0 218.0 218.0 0.61 357.4 500 2+17 820
Max Range -50 218.0 268.0 0.61 357.4 500 1+52 667
Slower -50 200.0 250.0 0.62 322.6 500 2+00 645 Slowing dvery own in tailwind helps, marginally

Range Economy

Selecting an en course altitude and also speed significantly results the amount of fuel melted, however tright here are other costs that may outweigh the price of Jet-A. The significant airlines have actually lengthy well-known this and also that’s why some airline trip monitoring computers (FMC) incorpoprice a Cost Index (CI) as a performance initialization input. Boeing defines CI as the moment price of the aircraft separated by the fuel price. The time price contains the crew, maintenance programs and also simply about whatever else that is paid for by the hour. If the fuel is even more expensive than every little thing else, it pays to slow-moving down. If the “everything else” is more than the fuel, you may desire to speed up. Few business aircraft FMCs have CI entries, yet tright here are commercial options out tbelow, such as the Pilot Performance Advisory System (PPAS) obtainable at http://www.aasi.com.

You have the right to number a Cost Index of your own, please feel free to download my Range Economy Spcheck out Sheet and customize it for your procedure. If your numbers prove me wrong, please let me understand. Until then, right here are a few formulas:

Speed of Sound

If your normal cruise speed is flown in Mach numbers, your initially action is to convert that to True Airspeed (TAS) and also to carry out that you need to uncover the rate of sound at your tarobtain altitude.

If Altitude > 36,089, then Speed of Sound = 573 nm/hr

Otherwise

Speed of Sound = 29.06 518.7 - 3.57 Altitude 1000 Mach to TAS

If you are cruising in Mach, you should convert that to TAS.

See more: Which Of The Following Lines From A Way Of Talking Quick Check Flashcards

TAS = Mach * Speed of Sound Range Economy

You can uncover your array economic climate given the adhering to variables:

FF — Fuel Flow (pounds per hour), average in cruise

FC — Fuel Cost ($ per gallon)

FD — Fuel Density (pounds per gallon)

D — Distance to cruise (because the climb and descent fuel will be about the exact same, we take into consideration only the cruise portion)

TAS — True Air Speed in the time of cruise

VA — Variable Airframe prices ($ per hour)

VC — Variable Crew prices ($ per hour)

VE — Variable Engine costs ($ per hour)

WF — Wind Factor (positive numbers for headwinds, negative for tailwinds)

Total Cost = ( D TAS - WF ) X ( FF ( FC FD ) + VA+ VC + VE ) G450 Example

If you take into consideration a G450 cruising at 37,000 feet on a 3,000 nm leg, in a 100 knot headwind at 70,000 lbs and ISA, average fuel flow will certainly be 2,966 PPH (M 0.77), 3,178 PPH (M 0.80), and also 3,593 PPH (M 0.83). If the fuel costs $3 per gallon and has actually a density of 6.5 gallons per pound, and the variable prices are as shown:

Mach No Variable Costs $1,000 Variable Costs $3,000 Variable Costs
M 0.77 $12,035 $20,828 $38,413
M 0.80 $12,278 $20,648 $37,389
M 0.83 $13,245 $21,233 $37,207

As fuel expenses drop, other variable prices end up being increasingly important. In the instance displayed it does not make sense to speed up in a headwind when there are no various other variable prices. That renders sense, the quicker you go the more fuel you burn. But as variable expenses other than fuel rise, tright here comes a allude where it pays to rate up bereason fuel would be cheaper than the various other variable prices. Let"s say you paid you crew by the hour and also had actually a maintenance program billable by the hour. If those variable expenses pertained to $3,000 per hour you end up better off increasing, as presented.