36:
93:
4406:
1594:
4210:
4827:
While the peak value of a specific range would provide maximum range operation, long-range cruise operation is generally recommended at a slightly higher airspeed. Most long-range cruise operations are conducted at the flight condition that provides 99 percent of the absolute maximum specific range.
96:
Maximum
Endurance and Range versus airspeed. The maximum endurance condition would be obtained at the point of minimum power required since this would require the lowest fuel flow to keep the airplane in a steady, level flight. Maximum range condition would occur where the ratio of speed to power
167:
For most unpowered aircraft, the maximum flight time is variable, limited by available daylight hours, aircraft design (performance), weather conditions, aircraft potential energy, and pilot endurance. Therefore, the range equation can only be calculated exactly for powered aircraft. It will be
1001:
is the fuel consumption rate, is called the specific range (= range per unit mass of fuel; S.I. units: m/kg). The specific range can now be determined as though the airplane is in quasi-steady-state flight. Here, a difference between jet and propeller-driven aircraft has to be noticed.
2435:
2594:
3799:
911:
3636:
1729:
136:
Some aircraft can gain energy while airborne through the environment (e.g. collecting solar energy or through rising air currents from mechanical or thermal lifting) or from in-flight refueling. These aircraft could theoretically have an infinite range.
2266:
1421:
4659:
4818:
4505:
2805:
3291:
is constant as the aircraft weight decreases. This is generally not a good approximation because a significant portion (e.g. 5% to 10%) of the fuel flow does not produce thrust and is instead required for engine "accessories" such as
526:
3191:
4401:{\displaystyle \eta _{\text{struc}}=\ln {\frac {{\widehat {W}}_{1}}{{\widehat {W}}_{2}}}=\ln \left(1+{\frac {{W}_{\text{fuel}}}{{\widehat {W}}_{2}}}\right)=-\ln \left(1-{\frac {{W}_{\text{fuel}}}{{\widehat {W}}_{1}}}\right)}
2299:
4161:
4719:
2467:
3653:
739:
3503:
has been adjusted down and the virtual aircraft weight has been adjusted up to maintain the proper fuel flow while making the adjusted thrust specific fuel consumption truly constant (not a function of virtual weight).
3495:
4068:
3510:
619:
1647:
5059:
405:
1857:
1432:
3898:
3283:
2075:
1643:
1162:
2173:
2140:
1282:
3418:
1306:
2855:
159:
is a related measure based on the maximum distance a warplane can travel from its base of operations, accomplish some objective, and return to its original airfield with minimal reserves.
4559:
4169:. A physical interpretation is a height that a quantity of fuel could lift itself in the Earth's gravity field (assumed constant) by converting its chemical energy into potential energy.
1982:
4760:
2973:
4437:
1919:
2692:
3975:
133:
multiplied by the maximum time in the air. The fuel time limit for powered aircraft is fixed by the available fuel (considering reserve fuel requirements) and rate of consumption.
4095:
1783:
4943:
4748:
4002:
3933:
3026:
1429:
for range, it has to be noted that specific range and fuel weight flow rate can be related to the characteristics of the airplane and propulsion system; if these are constant:
432:
2926:
3640:
The above equation combines the energy characteristics of the fuel with the efficiency of the jet engine. It is often useful to separate these terms. Doing so completes the
3368:
3341:
1603:
An electric aircraft with battery power only will have the same mass at takeoff and landing. The logarithmic term with weight ratios is replaced by the direct ratio between
255:
1210:
4540:
1048:
959:
1075:
4103:
4670:
4194:
3829:
3080:
3053:
2882:
2160:
1756:
1105:
729:
702:
675:
648:
309:
282:
4542:
may be expressed as the product of individual operational efficiency terms. For example, average wind may be accounted for using the relationship between average
2643:
1811:
2683:
2663:
2455:
2294:
999:
979:
546:
427:
329:
206:
186:
3422:
3209:
It is possible to improve the accuracy of the
Breguet range equation by recognizing the limitations of the conventionally used relationships for fuel flow:
3092:
4961:
551:
4410:
As an example, with an overall engine efficiency of 40%, a lift-to-drag ratio of 18:1, and a structural efficiency of 50%, the cruise range would be
334:
2616:
requires the aircraft to climb (as weight decreases due to fuel burn), without changing the value of the local speed of sound. In this case:
3212:
2004:
4008:
2596:
where the compressibility on the aerodynamic characteristics of the airplane are neglected as the flight speed reduces during the flight.
2430:{\displaystyle R={\frac {1}{c_{T}}}{\sqrt {{\frac {C_{L}}{C_{D}^{2}}}{\frac {2}{g\rho S}}}}\int _{W_{2}}^{W_{1}}{\frac {1}{\sqrt {W}}}dW;}
2167:
2589:{\displaystyle R={\frac {2}{c_{T}}}{\sqrt {{\frac {C_{L}}{C_{D}^{2}}}{\frac {2}{g\rho S}}}}\left({\sqrt {W_{1}}}-{\sqrt {W_{2}}}\right)}
4932:
3794:{\displaystyle R=Z_{f}{\frac {aM}{Z_{f}g{\widehat {c}}_{T}}}{\frac {C_{L}}{C_{D}}}\ln {\frac {{\widehat {W}}_{1}}{{\widehat {W}}_{2}}}}
1110:
2086:
1221:
906:{\displaystyle R=\int _{t_{1}}^{t_{2}}{\frac {dR}{dt}}dt=\int _{W_{1}}^{W_{2}}-{\frac {V}{F}}dW=\int _{W_{2}}^{W_{1}}{\frac {V}{F}}dW}
151:
load, optionally with extra fuel tanks and minimum equipment. It refers to the transport of aircraft without any passengers or cargo.
3375:
1928:
129:
range depends on factors such as cross-country speed and environmental conditions. The range can be seen as the cross-country
4997:
3631:{\displaystyle R={\frac {aM}{g{\widehat {c}}_{T}}}{\frac {C_{L}}{C_{D}}}\ln {\frac {{\widehat {W}}_{1}}{{\widehat {W}}_{2}}}}
1816:
3840:
4828:
The advantage of such operation is that one percent of the range is traded for three to five percent higher cruise speed.
1606:
1010:
With propeller-driven propulsion, the level flight speed at a number of airplane weights from the equilibrium condition
5039:
5005:
4915:
4751:
4100:
giving the final form of the theoretical range equation (not including operational factors such as wind and routing)
1724:{\displaystyle R=E^{*}{\frac {1}{g}}\eta _{\text{total}}{\frac {L}{D}}{\frac {W_{\text{battery}}}{W_{\text{total}}}}}
79:
57:
211:
50:
5022:
3500:
3288:
1992:
1169:
2810:
4967:
3311:
This can be accounted for by extending the assumed fuel flow formula in a simple way where an "adjusted" virtual
1078:
2931:
1589:{\displaystyle R={\frac {\eta _{j}}{gc_{p}}}{\frac {C_{L}}{C_{D}}}\ln {\frac {W_{1}}{W_{2}}}=V(L/D)IspLn(Wi/Wf)}
1874:
5081:
3939:
4971:
4862:
5052:
5049:
4073:
2619:
1761:
4726:
3980:
2261:{\displaystyle {\frac {V}{F}}={\frac {1}{c_{T}}}{\sqrt {{\frac {C_{L}}{C_{D}^{2}}}{\frac {2}{\rho SW}}}}}
17:
3911:
1050:
has to be noted. To each flight velocity, there corresponds a particular value of propulsive efficiency
4886:
2978:
1416:{\displaystyle R={\frac {\eta _{j}}{gc_{p}}}{\frac {C_{L}}{C_{D}}}\int _{W_{2}}^{W_{1}}{\frac {dW}{W}}}
4654:{\displaystyle \eta _{\text{wind}}={\frac {TAS-HW_{\text{avg}}}{TAS}}={\frac {GS_{\text{avg}}}{TAS}}}
2891:
4813:{\displaystyle \eta _{\text{ops}}=\eta _{\text{route}}\eta _{\text{wind}}\eta _{\text{temp}}\cdots }
3346:
3317:
44:
4500:{\displaystyle R=Z_{f}\eta _{\text{eng}}\eta _{\text{aero}}\eta _{\text{struc}}\eta _{\text{ops}}}
4847:
4512:
1013:
97:
required is greatest. The maximum range condition is obtained at maximum lift/drag ratio (L/DMAX)
2800:{\displaystyle R={\frac {aM}{gc_{T}}}{\frac {C_{L}}{C_{D}}}\int _{W_{2}}^{W_{1}}{\frac {dW}{W}}}
937:
4867:
4842:
4431:
1053:
61:
4664:
3901:
3641:
3312:
3198:
1430:
125:
energy storage capacity (chemical or electrical) considering both weight and volume limits.
5076:
4430:
The range equation may be further extended to consider operational factors by including an
4172:
3807:
3305:
3297:
3058:
3031:
2860:
2145:
1734:
1083:
707:
680:
653:
626:
287:
260:
521:{\displaystyle {\frac {dW}{dR}}={\frac {\frac {dW}{dt}}{\frac {dR}{dt}}}=-{\frac {F}{V}},}
8:
4857:
3832:
1788:
1426:
4872:
4166:
2668:
2648:
2440:
2279:
1215:
984:
964:
531:
412:
314:
191:
171:
126:
5045:
1785:
the total efficiency (typically 0.7-0.8 for batteries, motor, gearbox and propeller),
5035:
5001:
4993:
4911:
4201:
1871:
can be derived likewise. Now, quasi-steady level flight is assumed. The relationship
4723:
Off-nominal temperatures may be accounted for with a temperature efficiency factor
3186:{\textstyle R={\frac {aM}{gc_{T}}}{\frac {C_{L}}{C_{D}}}\ln {\frac {W_{1}}{W_{2}}}}
1996:
1297:
118:
4852:
2461:
1758:
is the energy per mass of the battery (e.g. 150-200 Wh/kg for Li-ion batteries),
4156:{\displaystyle R=Z_{f}\eta _{\text{eng}}\eta _{\text{aero}}\eta _{\text{struc}}}
2612:
is approximately constant, hence flying at a fixed angle of attack and constant
4714:{\displaystyle \eta _{\text{route}}={\frac {D_{\text{GC}}}{D_{\text{actual}}}}}
3905:
3293:
2686:
2609:
4757:
All of the operational efficiency factors may be collected into a single term
1303:
The range integral, assuming flight at a constant lift to drag ratio, becomes
92:
5070:
5012:
4877:
4837:
4547:
3083:
623:
It follows that the range is obtained from the definite integral below, with
155:
122:
4543:
4207:
There are two useful alternative ways to express the structural efficiency
2605:
2080:
1868:
144:
130:
4421:) (40%) (18) (50%) = 8,553.6 nmi (15,841.3 km)
3645:
2613:
2163:
3490:{\displaystyle F={\widehat {c}}_{T}{\frac {C_{D}}{C_{L}}}{\widehat {W}}}
4881:
1214:
Thrust power is the speed multiplied by the drag, is obtained from the
3301:
4063:{\displaystyle \ln {\frac {{\widehat {W}}_{1}}{{\widehat {W}}_{2}}}}
4551:
4197:
311:
the mass of the fuel, the fuel consumption rate per unit time flow
106:
5018:
Blacksburg: VA: University
Libraries at Virginia Tech. CC BY 4.0.
114:
110:
614:{\displaystyle {\frac {dR}{dt}}=-{\frac {V}{F}}{\frac {dW}{dt}}}
1922:
168:
derived for both propeller and jet aircraft. If the total mass
3343:
is defined by adding a constant additional "accessory" weight
3086:
of air at constant pressure and constant volume respectively.
1166:
The corresponding fuel weight flow rates can be computed now:
3644:
of the range equation into fundamental design disciplines of
2464:
and a constant specific fuel consumption, the range becomes:
5055:, "Chapter 13.3 Aircraft Range: the Breguet Range Equation".
4200:
is 2,376 nautical miles (4,400 km) or about 69% of the
1813:
lift over drag (typically around 18), and the weight ratio
148:
1300:(its exact value varies, but it averages 9.81 m/s).
2608:(altitude approximately between 11 and 20 km), the
2599:
400:{\displaystyle -{\frac {dW_{f}}{dt}}=-{\frac {dW}{dt}}.}
27:
Distance an aircraft can fly between takeoff and landing
1852:{\displaystyle {W_{\text{battery}}}/{W_{\text{total}}}}
3893:{\displaystyle {\frac {aM}{Z_{f}g{\widehat {c}}_{T}}}}
3287:
In the
Breguet range equation, it is assumed that the
3095:
2934:
2813:
940:
5026:. "Range and endurance: Breguet's equation", page 25.
4763:
4729:
4673:
4562:
4515:
4440:
4213:
4175:
4106:
4076:
4011:
3983:
3942:
3914:
3843:
3810:
3656:
3513:
3425:
3378:
3349:
3320:
3278:{\displaystyle F=c_{T}T=c_{T}{\frac {C_{D}}{C_{L}}}W}
3215:
3061:
3034:
2981:
2894:
2863:
2695:
2671:
2651:
2622:
2470:
2443:
2302:
2282:
2176:
2148:
2089:
2070:{\displaystyle F=c_{T}T=c_{T}{\frac {C_{D}}{C_{L}}}W}
2007:
1931:
1877:
1819:
1791:
1764:
1737:
1650:
1609:
1435:
1309:
1224:
1172:
1113:
1086:
1056:
1016:
987:
967:
742:
710:
683:
656:
629:
554:
534:
435:
415:
337:
317:
290:
263:
214:
194:
174:
143:
means the maximum range that an aircraft engaged in
1638:{\displaystyle W_{\text{battery}}/W_{\text{total}}}
4812:
4742:
4713:
4653:
4534:
4499:
4400:
4188:
4155:
4089:
4062:
3996:
3969:
3927:
3892:
3823:
3793:
3630:
3507:Then, the modified Breguet range equation becomes
3489:
3412:
3362:
3335:
3277:
3204:
3185:
3074:
3047:
3020:
2967:
2920:
2876:
2849:
2799:
2689:. W is the weight. The range equation reduces to:
2677:
2657:
2637:
2588:
2449:
2429:
2288:
2260:
2154:
2134:
2069:
1976:
1913:
1851:
1805:
1777:
1750:
1723:
1637:
1588:
1415:
1276:
1204:
1156:
1099:
1069:
1042:
993:
973:
953:
905:
723:
696:
669:
642:
613:
540:
520:
421:
409:The rate of change of aircraft mass with distance
399:
323:
303:
276:
249:
200:
180:
4988:Anderson, David W. & Scott Eberhardt (2010).
4165:The geopotential energy height of the fuel is an
1157:{\displaystyle P_{br}={\frac {P_{a}}{\eta _{j}}}}
5068:
3977:is the aerodynamic efficiency (non-dimensional)
2135:{\displaystyle {\frac {1}{2}}\rho V^{2}SC_{L}=W}
1277:{\displaystyle P_{a}=V{\frac {C_{D}}{C_{L}}}Wg;}
4070:is the structural efficiency (non-dimensional)
3413:{\displaystyle {\widehat {W}}=W+W_{\text{acc}}}
2296:is varying, the range (in kilometers) becomes:
1995:, so that rate of fuel flow is proportional to
4933:"Electric Flight – Potential and Limitations"
4425:
2850:{\textstyle a={\sqrt {{\frac {7}{5}}R_{s}T}}}
1107:. The successive engine powers can be found:
1977:{\displaystyle T=D={\frac {C_{D}}{C_{L}}}W;}
677:the start and finish times respectively and
2968:{\textstyle \gamma ={\frac {c_{p}}{c_{v}}}}
4963:Pilot's Handbook of Aeronautical Knowledge
4663:Routing efficiency may be defined as the
2460:When cruising at a fixed height, a fixed
1914:{\displaystyle D={\frac {C_{D}}{C_{L}}}W}
80:Learn how and when to remove this message
4970:. 2016-08-24. p. 10. Archived from
4930:
2170:, the specific range is found equal to:
147:can achieve. This usually means maximum
91:
43:This article includes a list of general
4910:(first ed.). Osprey. p. 221.
14:
5069:
3970:{\displaystyle {\frac {C_{L}}{C_{D}}}}
731:the initial and final aircraft masses
5014:Aerodynamics and Aircraft Performance
4905:
4667:divided by the actual route distance
4550:(TAS, assumed constant), and average
2884:is the specific heat constant of air
2600:Cruise/climb (Breguet range equation)
1005:
188:of the aircraft at a particular time
4990:Understanding Flight, Second Edition
4960:"Chapter 11: Aircraft Performance".
4090:{\displaystyle \eta _{\text{struc}}}
1778:{\displaystyle \eta _{\text{total}}}
1598:
1288:is the weight (force in newtons, if
733:
29:
4743:{\displaystyle \eta _{\text{temp}}}
3997:{\displaystyle \eta _{\text{aero}}}
3197:after the French aviation pioneer,
1991:Jet engines are characterized by a
24:
3928:{\displaystyle \eta _{\text{eng}}}
2888:(based on aviation standards) and
2604:For jet aircraft operating in the
49:it lacks sufficient corresponding
25:
5093:
4982:
4949:from the original on Apr 5, 2024.
4931:Hepperle, Martin (October 2012).
4752:International Standard Atmosphere
3021:{\displaystyle c_{p}=c_{v}+R_{s}}
1862:
929:
5032:Elements of Airplane Performance
3501:thrust specific fuel consumption
3289:thrust specific fuel consumption
1993:thrust specific fuel consumption
34:
4968:Federal Aviation Administration
3205:Modified Breguet range equation
2921:{\displaystyle \gamma =7/5=1.4}
4953:
4924:
4899:
4434:("ops" for flight operations)
3363:{\displaystyle W_{\text{acc}}}
3336:{\displaystyle {\widehat {W}}}
2665:is the cruise Mach number and
1583:
1563:
1545:
1531:
250:{\displaystyle W=W_{0}+W_{f},}
13:
1:
5053:Thermodynamics and Propulsion
5011:Marchman, James, III (2021).
4892:
1205:{\displaystyle F=c_{p}P_{br}}
162:
4863:Energy conversion efficiency
4750:(e.g. 99% at 10 deg C above
7:
5034:. Delft University Press.
4966:(FAA-H-8083-25B ed.).
4831:
4822:
4535:{\displaystyle \eta _{ops}}
4509:The operational efficiency
2272:
1292:is the mass in kilograms);
1043:{\displaystyle P_{a}=P_{r}}
954:{\textstyle {\frac {V}{F}}}
919:
105:is the maximum distance an
10:
5098:
4426:Operational Considerations
3833:geopotential energy height
284:is the zero-fuel mass and
5046:"Prof. Z. S. Spakovszky".
1079:specific fuel consumption
1070:{\displaystyle \eta _{j}}
4908:A Dictionary of Aviation
4906:Wragg, David W. (1973).
121:range is limited by the
4887:Newton's laws of motion
4848:Endurance (aeronautics)
1925:can now be written as:
548:is the speed), so that
64:more precise citations.
4868:Jet engine performance
4843:Flight distance record
4814:
4744:
4715:
4655:
4536:
4501:
4432:operational efficiency
4402:
4190:
4157:
4091:
4064:
3998:
3971:
3929:
3894:
3825:
3795:
3632:
3491:
3414:
3364:
3337:
3279:
3195:Breguet range equation
3187:
3076:
3049:
3022:
2969:
2922:
2878:
2851:
2801:
2679:
2659:
2639:
2590:
2451:
2431:
2290:
2262:
2156:
2136:
2071:
1988:is a force in newtons
1978:
1915:
1859:typically around 0.3.
1853:
1807:
1779:
1752:
1725:
1639:
1590:
1417:
1278:
1206:
1158:
1101:
1071:
1044:
995:
975:
955:
907:
725:
698:
671:
644:
615:
542:
522:
423:
401:
325:
305:
278:
251:
202:
182:
98:
4815:
4745:
4716:
4665:great-circle distance
4656:
4537:
4502:
4403:
4191:
4189:{\displaystyle Z_{f}}
4158:
4092:
4065:
3999:
3972:
3930:
3902:propulsive efficiency
3895:
3826:
3824:{\displaystyle Z_{f}}
3796:
3642:nondimensionalization
3633:
3492:
3415:
3365:
3338:
3313:aircraft gross weight
3298:electrical generators
3280:
3199:Louis Charles Breguet
3188:
3077:
3075:{\displaystyle c_{v}}
3050:
3048:{\displaystyle c_{p}}
3023:
2970:
2923:
2879:
2877:{\displaystyle R_{s}}
2852:
2802:
2680:
2660:
2640:
2591:
2452:
2432:
2291:
2270:Inserting this into (
2263:
2157:
2155:{\displaystyle \rho }
2137:
2072:
1999:, rather than power.
1979:
1916:
1854:
1808:
1780:
1753:
1751:{\displaystyle E^{*}}
1726:
1640:
1591:
1418:
1279:
1207:
1159:
1102:
1100:{\displaystyle c_{p}}
1072:
1045:
996:
976:
956:
908:
726:
724:{\displaystyle W_{2}}
699:
697:{\displaystyle W_{1}}
672:
670:{\displaystyle t_{2}}
645:
643:{\displaystyle t_{1}}
616:
543:
523:
424:
402:
326:
306:
304:{\displaystyle W_{f}}
279:
277:{\displaystyle W_{0}}
252:
203:
183:
95:
5082:Aircraft performance
4761:
4754:(ISA) temperature).
4727:
4671:
4560:
4513:
4438:
4211:
4173:
4104:
4074:
4009:
3981:
3940:
3912:
3841:
3808:
3654:
3511:
3423:
3376:
3347:
3318:
3306:cabin pressurization
3213:
3193:, also known as the
3093:
3059:
3032:
2979:
2932:
2892:
2861:
2811:
2693:
2669:
2649:
2638:{\displaystyle V=aM}
2620:
2468:
2441:
2300:
2280:
2276:) and assuming only
2174:
2146:
2087:
2005:
1929:
1875:
1817:
1789:
1762:
1735:
1648:
1607:
1433:
1307:
1222:
1170:
1111:
1084:
1054:
1014:
985:
965:
938:
740:
708:
681:
654:
627:
552:
532:
433:
413:
335:
315:
288:
261:
212:
192:
172:
5030:Ruijgrok, G. J. J.
5024:Aircraft propulsion
5021:Martinez, Isidoro.
4858:Geopotential height
2781:
2522:
2405:
2354:
2235:
1806:{\displaystyle L/D}
1427:analytic expression
1397:
886:
835:
777:
4873:Lift-to-drag ratio
4810:
4740:
4711:
4651:
4532:
4497:
4398:
4186:
4167:intensive property
4153:
4087:
4060:
3994:
3967:
3925:
3890:
3821:
3791:
3628:
3487:
3410:
3360:
3333:
3275:
3183:
3072:
3045:
3018:
2965:
2918:
2886:287.16 J/kg K
2874:
2847:
2797:
2753:
2675:
2655:
2635:
2586:
2508:
2447:
2427:
2377:
2340:
2286:
2258:
2221:
2152:
2132:
2067:
1974:
1911:
1849:
1803:
1775:
1748:
1721:
1635:
1586:
1413:
1369:
1274:
1216:lift-to-drag ratio
1202:
1154:
1097:
1067:
1040:
1006:Propeller aircraft
991:
981:is the speed, and
971:
951:
903:
858:
807:
749:
721:
694:
667:
640:
611:
538:
518:
419:
397:
321:
301:
274:
247:
198:
178:
127:Unpowered aircraft
101:The maximal total
99:
4998:978-0-07-162697-2
4804:
4794:
4784:
4771:
4737:
4709:
4706:
4696:
4681:
4649:
4634:
4616:
4601:
4570:
4494:
4484:
4474:
4464:
4391:
4382:
4369:
4328:
4319:
4306:
4273:
4264:
4245:
4221:
4150:
4140:
4130:
4084:
4058:
4049:
4030:
3991:
3965:
3922:
3888:
3878:
3789:
3780:
3761:
3741:
3717:
3707:
3626:
3617:
3598:
3578:
3554:
3544:
3484:
3473:
3442:
3407:
3388:
3357:
3330:
3270:
3181:
3151:
3127:
3082:are the specific
2963:
2845:
2830:
2795:
2751:
2727:
2678:{\displaystyle a}
2658:{\displaystyle M}
2579:
2562:
2543:
2541:
2523:
2492:
2450:{\displaystyle W}
2416:
2415:
2375:
2373:
2355:
2324:
2289:{\displaystyle W}
2256:
2254:
2236:
2205:
2185:
2098:
2062:
1966:
1906:
1845:
1828:
1772:
1719:
1716:
1706:
1695:
1684:
1675:
1632:
1617:
1599:Electric aircraft
1523:
1493:
1469:
1411:
1367:
1343:
1263:
1152:
994:{\displaystyle F}
974:{\displaystyle V}
949:
927:
926:
895:
847:
796:
609:
589:
573:
541:{\displaystyle V}
513:
497:
496:
478:
454:
422:{\displaystyle R}
392:
366:
324:{\displaystyle F}
201:{\displaystyle t}
181:{\displaystyle W}
90:
89:
82:
16:(Redirected from
5089:
4976:
4975:
4957:
4951:
4950:
4948:
4937:
4928:
4922:
4921:
4903:
4819:
4817:
4816:
4811:
4806:
4805:
4802:
4796:
4795:
4792:
4786:
4785:
4782:
4773:
4772:
4769:
4749:
4747:
4746:
4741:
4739:
4738:
4735:
4720:
4718:
4717:
4712:
4710:
4708:
4707:
4704:
4698:
4697:
4694:
4688:
4683:
4682:
4679:
4660:
4658:
4657:
4652:
4650:
4648:
4637:
4636:
4635:
4632:
4622:
4617:
4615:
4604:
4603:
4602:
4599:
4577:
4572:
4571:
4568:
4554:(HW) component.
4541:
4539:
4538:
4533:
4531:
4530:
4506:
4504:
4503:
4498:
4496:
4495:
4492:
4486:
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4482:
4476:
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4472:
4466:
4465:
4462:
4456:
4455:
4422:
4420:
4407:
4405:
4404:
4399:
4397:
4393:
4392:
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4389:
4384:
4383:
4375:
4371:
4370:
4367:
4365:
4359:
4334:
4330:
4329:
4327:
4326:
4321:
4320:
4312:
4308:
4307:
4304:
4302:
4296:
4274:
4272:
4271:
4266:
4265:
4257:
4253:
4252:
4247:
4246:
4238:
4234:
4223:
4222:
4219:
4195:
4193:
4192:
4187:
4185:
4184:
4162:
4160:
4159:
4154:
4152:
4151:
4148:
4142:
4141:
4138:
4132:
4131:
4128:
4122:
4121:
4096:
4094:
4093:
4088:
4086:
4085:
4082:
4069:
4067:
4066:
4061:
4059:
4057:
4056:
4051:
4050:
4042:
4038:
4037:
4032:
4031:
4023:
4019:
4003:
4001:
4000:
3995:
3993:
3992:
3989:
3976:
3974:
3973:
3968:
3966:
3964:
3963:
3954:
3953:
3944:
3934:
3932:
3931:
3926:
3924:
3923:
3920:
3899:
3897:
3896:
3891:
3889:
3887:
3886:
3885:
3880:
3879:
3871:
3864:
3863:
3853:
3845:
3835:of the fuel (km)
3830:
3828:
3827:
3822:
3820:
3819:
3800:
3798:
3797:
3792:
3790:
3788:
3787:
3782:
3781:
3773:
3769:
3768:
3763:
3762:
3754:
3750:
3742:
3740:
3739:
3730:
3729:
3720:
3718:
3716:
3715:
3714:
3709:
3708:
3700:
3693:
3692:
3682:
3674:
3672:
3671:
3637:
3635:
3634:
3629:
3627:
3625:
3624:
3619:
3618:
3610:
3606:
3605:
3600:
3599:
3591:
3587:
3579:
3577:
3576:
3567:
3566:
3557:
3555:
3553:
3552:
3551:
3546:
3545:
3537:
3529:
3521:
3496:
3494:
3493:
3488:
3486:
3485:
3477:
3474:
3472:
3471:
3462:
3461:
3452:
3450:
3449:
3444:
3443:
3435:
3419:
3417:
3416:
3411:
3409:
3408:
3405:
3390:
3389:
3381:
3369:
3367:
3366:
3361:
3359:
3358:
3355:
3342:
3340:
3339:
3334:
3332:
3331:
3323:
3284:
3282:
3281:
3276:
3271:
3269:
3268:
3259:
3258:
3249:
3247:
3246:
3231:
3230:
3192:
3190:
3189:
3184:
3182:
3180:
3179:
3170:
3169:
3160:
3152:
3150:
3149:
3140:
3139:
3130:
3128:
3126:
3125:
3124:
3111:
3103:
3081:
3079:
3078:
3073:
3071:
3070:
3054:
3052:
3051:
3046:
3044:
3043:
3027:
3025:
3024:
3019:
3017:
3016:
3004:
3003:
2991:
2990:
2974:
2972:
2971:
2966:
2964:
2962:
2961:
2952:
2951:
2942:
2927:
2925:
2924:
2919:
2908:
2887:
2883:
2881:
2880:
2875:
2873:
2872:
2856:
2854:
2853:
2848:
2846:
2841:
2840:
2831:
2823:
2821:
2806:
2804:
2803:
2798:
2796:
2791:
2783:
2780:
2779:
2778:
2768:
2767:
2766:
2752:
2750:
2749:
2740:
2739:
2730:
2728:
2726:
2725:
2724:
2711:
2703:
2684:
2682:
2681:
2676:
2664:
2662:
2661:
2656:
2644:
2642:
2641:
2636:
2595:
2593:
2592:
2587:
2585:
2581:
2580:
2578:
2577:
2568:
2563:
2561:
2560:
2551:
2544:
2542:
2540:
2526:
2524:
2521:
2516:
2507:
2506:
2497:
2495:
2493:
2491:
2490:
2478:
2456:
2454:
2453:
2448:
2436:
2434:
2433:
2428:
2417:
2411:
2407:
2404:
2403:
2402:
2392:
2391:
2390:
2376:
2374:
2372:
2358:
2356:
2353:
2348:
2339:
2338:
2329:
2327:
2325:
2323:
2322:
2310:
2295:
2293:
2292:
2287:
2267:
2265:
2264:
2259:
2257:
2255:
2253:
2239:
2237:
2234:
2229:
2220:
2219:
2210:
2208:
2206:
2204:
2203:
2191:
2186:
2178:
2161:
2159:
2158:
2153:
2141:
2139:
2138:
2133:
2125:
2124:
2112:
2111:
2099:
2091:
2076:
2074:
2073:
2068:
2063:
2061:
2060:
2051:
2050:
2041:
2039:
2038:
2023:
2022:
1983:
1981:
1980:
1975:
1967:
1965:
1964:
1955:
1954:
1945:
1920:
1918:
1917:
1912:
1907:
1905:
1904:
1895:
1894:
1885:
1858:
1856:
1855:
1850:
1848:
1847:
1846:
1843:
1836:
1831:
1830:
1829:
1826:
1812:
1810:
1809:
1804:
1799:
1784:
1782:
1781:
1776:
1774:
1773:
1770:
1757:
1755:
1754:
1749:
1747:
1746:
1730:
1728:
1727:
1722:
1720:
1718:
1717:
1714:
1708:
1707:
1704:
1698:
1696:
1688:
1686:
1685:
1682:
1676:
1668:
1666:
1665:
1644:
1642:
1641:
1636:
1634:
1633:
1630:
1624:
1619:
1618:
1615:
1595:
1593:
1592:
1587:
1576:
1541:
1524:
1522:
1521:
1512:
1511:
1502:
1494:
1492:
1491:
1482:
1481:
1472:
1470:
1468:
1467:
1466:
1453:
1452:
1443:
1422:
1420:
1419:
1414:
1412:
1407:
1399:
1396:
1395:
1394:
1384:
1383:
1382:
1368:
1366:
1365:
1356:
1355:
1346:
1344:
1342:
1341:
1340:
1327:
1326:
1317:
1298:standard gravity
1283:
1281:
1280:
1275:
1264:
1262:
1261:
1252:
1251:
1242:
1234:
1233:
1211:
1209:
1208:
1203:
1201:
1200:
1188:
1187:
1163:
1161:
1160:
1155:
1153:
1151:
1150:
1141:
1140:
1131:
1126:
1125:
1106:
1104:
1103:
1098:
1096:
1095:
1076:
1074:
1073:
1068:
1066:
1065:
1049:
1047:
1046:
1041:
1039:
1038:
1026:
1025:
1000:
998:
997:
992:
980:
978:
977:
972:
960:
958:
957:
952:
950:
942:
921:
912:
910:
909:
904:
896:
888:
885:
884:
883:
873:
872:
871:
848:
840:
834:
833:
832:
822:
821:
820:
797:
795:
787:
779:
776:
775:
774:
764:
763:
762:
734:
730:
728:
727:
722:
720:
719:
703:
701:
700:
695:
693:
692:
676:
674:
673:
668:
666:
665:
649:
647:
646:
641:
639:
638:
620:
618:
617:
612:
610:
608:
600:
592:
590:
582:
574:
572:
564:
556:
547:
545:
544:
539:
527:
525:
524:
519:
514:
506:
498:
495:
487:
479:
477:
469:
461:
460:
455:
453:
445:
437:
428:
426:
425:
420:
406:
404:
403:
398:
393:
391:
383:
375:
367:
365:
357:
356:
355:
342:
330:
328:
327:
322:
310:
308:
307:
302:
300:
299:
283:
281:
280:
275:
273:
272:
256:
254:
253:
248:
243:
242:
230:
229:
207:
205:
204:
199:
187:
185:
184:
179:
119:Powered aircraft
109:can fly between
85:
78:
74:
71:
65:
60:this article by
51:inline citations
38:
37:
30:
21:
5097:
5096:
5092:
5091:
5090:
5088:
5087:
5086:
5067:
5066:
4992:. McGraw-Hill.
4985:
4980:
4979:
4959:
4958:
4954:
4946:
4935:
4929:
4925:
4918:
4904:
4900:
4895:
4853:Specific energy
4834:
4825:
4801:
4797:
4791:
4787:
4781:
4777:
4768:
4764:
4762:
4759:
4758:
4734:
4730:
4728:
4725:
4724:
4703:
4699:
4693:
4689:
4687:
4678:
4674:
4672:
4669:
4668:
4638:
4631:
4627:
4623:
4621:
4605:
4598:
4594:
4578:
4576:
4567:
4563:
4561:
4558:
4557:
4520:
4516:
4514:
4511:
4510:
4491:
4487:
4481:
4477:
4471:
4467:
4461:
4457:
4451:
4447:
4439:
4436:
4435:
4428:
4423:
4418:
4413:
4385:
4374:
4373:
4372:
4366:
4361:
4360:
4358:
4351:
4347:
4322:
4311:
4310:
4309:
4303:
4298:
4297:
4295:
4288:
4284:
4267:
4256:
4255:
4254:
4248:
4237:
4236:
4235:
4233:
4218:
4214:
4212:
4209:
4208:
4180:
4176:
4174:
4171:
4170:
4147:
4143:
4137:
4133:
4127:
4123:
4117:
4113:
4105:
4102:
4101:
4081:
4077:
4075:
4072:
4071:
4052:
4041:
4040:
4039:
4033:
4022:
4021:
4020:
4018:
4010:
4007:
4006:
3988:
3984:
3982:
3979:
3978:
3959:
3955:
3949:
3945:
3943:
3941:
3938:
3937:
3919:
3915:
3913:
3910:
3909:
3900:is the overall
3881:
3870:
3869:
3868:
3859:
3855:
3854:
3846:
3844:
3842:
3839:
3838:
3815:
3811:
3809:
3806:
3805:
3783:
3772:
3771:
3770:
3764:
3753:
3752:
3751:
3749:
3735:
3731:
3725:
3721:
3719:
3710:
3699:
3698:
3697:
3688:
3684:
3683:
3675:
3673:
3667:
3663:
3655:
3652:
3651:
3620:
3609:
3608:
3607:
3601:
3590:
3589:
3588:
3586:
3572:
3568:
3562:
3558:
3556:
3547:
3536:
3535:
3534:
3530:
3522:
3520:
3512:
3509:
3508:
3476:
3475:
3467:
3463:
3457:
3453:
3451:
3445:
3434:
3433:
3432:
3424:
3421:
3420:
3404:
3400:
3380:
3379:
3377:
3374:
3373:
3354:
3350:
3348:
3345:
3344:
3322:
3321:
3319:
3316:
3315:
3294:hydraulic pumps
3264:
3260:
3254:
3250:
3248:
3242:
3238:
3226:
3222:
3214:
3211:
3210:
3207:
3175:
3171:
3165:
3161:
3159:
3145:
3141:
3135:
3131:
3129:
3120:
3116:
3112:
3104:
3102:
3094:
3091:
3090:
3084:heat capacities
3066:
3062:
3060:
3057:
3056:
3039:
3035:
3033:
3030:
3029:
3012:
3008:
2999:
2995:
2986:
2982:
2980:
2977:
2976:
2957:
2953:
2947:
2943:
2941:
2933:
2930:
2929:
2904:
2893:
2890:
2889:
2885:
2868:
2864:
2862:
2859:
2858:
2836:
2832:
2822:
2820:
2812:
2809:
2808:
2784:
2782:
2774:
2770:
2769:
2762:
2758:
2757:
2745:
2741:
2735:
2731:
2729:
2720:
2716:
2712:
2704:
2702:
2694:
2691:
2690:
2670:
2667:
2666:
2650:
2647:
2646:
2621:
2618:
2617:
2602:
2573:
2569:
2567:
2556:
2552:
2550:
2549:
2545:
2530:
2525:
2517:
2512:
2502:
2498:
2496:
2494:
2486:
2482:
2477:
2469:
2466:
2465:
2462:angle of attack
2457:is again mass.
2442:
2439:
2438:
2406:
2398:
2394:
2393:
2386:
2382:
2381:
2362:
2357:
2349:
2344:
2334:
2330:
2328:
2326:
2318:
2314:
2309:
2301:
2298:
2297:
2281:
2278:
2277:
2243:
2238:
2230:
2225:
2215:
2211:
2209:
2207:
2199:
2195:
2190:
2177:
2175:
2172:
2171:
2147:
2144:
2143:
2120:
2116:
2107:
2103:
2090:
2088:
2085:
2084:
2056:
2052:
2046:
2042:
2040:
2034:
2030:
2018:
2014:
2006:
2003:
2002:
1960:
1956:
1950:
1946:
1944:
1930:
1927:
1926:
1900:
1896:
1890:
1886:
1884:
1876:
1873:
1872:
1865:
1842:
1838:
1837:
1832:
1825:
1821:
1820:
1818:
1815:
1814:
1795:
1790:
1787:
1786:
1769:
1765:
1763:
1760:
1759:
1742:
1738:
1736:
1733:
1732:
1713:
1709:
1703:
1699:
1697:
1687:
1681:
1677:
1667:
1661:
1657:
1649:
1646:
1645:
1629:
1625:
1620:
1614:
1610:
1608:
1605:
1604:
1601:
1572:
1537:
1517:
1513:
1507:
1503:
1501:
1487:
1483:
1477:
1473:
1471:
1462:
1458:
1454:
1448:
1444:
1442:
1434:
1431:
1400:
1398:
1390:
1386:
1385:
1378:
1374:
1373:
1361:
1357:
1351:
1347:
1345:
1336:
1332:
1328:
1322:
1318:
1316:
1308:
1305:
1304:
1257:
1253:
1247:
1243:
1241:
1229:
1225:
1223:
1220:
1219:
1193:
1189:
1183:
1179:
1171:
1168:
1167:
1146:
1142:
1136:
1132:
1130:
1118:
1114:
1112:
1109:
1108:
1091:
1087:
1085:
1082:
1081:
1061:
1057:
1055:
1052:
1051:
1034:
1030:
1021:
1017:
1015:
1012:
1011:
1008:
986:
983:
982:
966:
963:
962:
941:
939:
936:
935:
932:
887:
879:
875:
874:
867:
863:
862:
839:
828:
824:
823:
816:
812:
811:
788:
780:
778:
770:
766:
765:
758:
754:
753:
741:
738:
737:
715:
711:
709:
706:
705:
688:
684:
682:
679:
678:
661:
657:
655:
652:
651:
634:
630:
628:
625:
624:
601:
593:
591:
581:
565:
557:
555:
553:
550:
549:
533:
530:
529:
505:
488:
480:
470:
462:
459:
446:
438:
436:
434:
431:
430:
414:
411:
410:
384:
376:
374:
358:
351:
347:
343:
341:
336:
333:
332:
316:
313:
312:
295:
291:
289:
286:
285:
268:
264:
262:
259:
258:
238:
234:
225:
221:
213:
210:
209:
193:
190:
189:
173:
170:
169:
165:
86:
75:
69:
66:
56:Please help to
55:
39:
35:
28:
23:
22:
15:
12:
11:
5:
5095:
5085:
5084:
5079:
5065:
5064:
5043:
5028:
5019:
5009:
4984:
4983:External links
4981:
4978:
4977:
4974:on 2023-06-20.
4952:
4923:
4916:
4897:
4896:
4894:
4891:
4890:
4889:
4884:
4875:
4870:
4865:
4860:
4855:
4850:
4845:
4840:
4833:
4830:
4824:
4821:
4809:
4800:
4790:
4780:
4776:
4767:
4733:
4702:
4692:
4686:
4677:
4647:
4644:
4641:
4630:
4626:
4620:
4614:
4611:
4608:
4597:
4593:
4590:
4587:
4584:
4581:
4575:
4566:
4529:
4526:
4523:
4519:
4490:
4480:
4470:
4460:
4454:
4450:
4446:
4443:
4427:
4424:
4412:
4396:
4388:
4381:
4378:
4364:
4357:
4354:
4350:
4346:
4343:
4340:
4337:
4333:
4325:
4318:
4315:
4301:
4294:
4291:
4287:
4283:
4280:
4277:
4270:
4263:
4260:
4251:
4244:
4241:
4232:
4229:
4226:
4217:
4202:Earth's radius
4183:
4179:
4146:
4136:
4126:
4120:
4116:
4112:
4109:
4098:
4097:
4080:
4055:
4048:
4045:
4036:
4029:
4026:
4017:
4014:
4004:
3987:
3962:
3958:
3952:
3948:
3935:
3918:
3906:nondimensional
3884:
3877:
3874:
3867:
3862:
3858:
3852:
3849:
3836:
3818:
3814:
3786:
3779:
3776:
3767:
3760:
3757:
3748:
3745:
3738:
3734:
3728:
3724:
3713:
3706:
3703:
3696:
3691:
3687:
3681:
3678:
3670:
3666:
3662:
3659:
3623:
3616:
3613:
3604:
3597:
3594:
3585:
3582:
3575:
3571:
3565:
3561:
3550:
3543:
3540:
3533:
3528:
3525:
3519:
3516:
3483:
3480:
3470:
3466:
3460:
3456:
3448:
3441:
3438:
3431:
3428:
3403:
3399:
3396:
3393:
3387:
3384:
3353:
3329:
3326:
3274:
3267:
3263:
3257:
3253:
3245:
3241:
3237:
3234:
3229:
3225:
3221:
3218:
3206:
3203:
3178:
3174:
3168:
3164:
3158:
3155:
3148:
3144:
3138:
3134:
3123:
3119:
3115:
3110:
3107:
3101:
3098:
3069:
3065:
3042:
3038:
3015:
3011:
3007:
3002:
2998:
2994:
2989:
2985:
2960:
2956:
2950:
2946:
2940:
2937:
2928:(derived from
2917:
2914:
2911:
2907:
2903:
2900:
2897:
2871:
2867:
2844:
2839:
2835:
2829:
2826:
2819:
2816:
2794:
2790:
2787:
2777:
2773:
2765:
2761:
2756:
2748:
2744:
2738:
2734:
2723:
2719:
2715:
2710:
2707:
2701:
2698:
2687:speed of sound
2674:
2654:
2634:
2631:
2628:
2625:
2610:speed of sound
2601:
2598:
2584:
2576:
2572:
2566:
2559:
2555:
2548:
2539:
2536:
2533:
2529:
2520:
2515:
2511:
2505:
2501:
2489:
2485:
2481:
2476:
2473:
2446:
2426:
2423:
2420:
2414:
2410:
2401:
2397:
2389:
2385:
2380:
2371:
2368:
2365:
2361:
2352:
2347:
2343:
2337:
2333:
2321:
2317:
2313:
2308:
2305:
2285:
2252:
2249:
2246:
2242:
2233:
2228:
2224:
2218:
2214:
2202:
2198:
2194:
2189:
2184:
2181:
2151:
2131:
2128:
2123:
2119:
2115:
2110:
2106:
2102:
2097:
2094:
2066:
2059:
2055:
2049:
2045:
2037:
2033:
2029:
2026:
2021:
2017:
2013:
2010:
1973:
1970:
1963:
1959:
1953:
1949:
1943:
1940:
1937:
1934:
1910:
1903:
1899:
1893:
1889:
1883:
1880:
1864:
1863:Jet propulsion
1861:
1841:
1835:
1824:
1802:
1798:
1794:
1768:
1745:
1741:
1712:
1702:
1694:
1691:
1680:
1674:
1671:
1664:
1660:
1656:
1653:
1628:
1623:
1613:
1600:
1597:
1585:
1582:
1579:
1575:
1571:
1568:
1565:
1562:
1559:
1556:
1553:
1550:
1547:
1544:
1540:
1536:
1533:
1530:
1527:
1520:
1516:
1510:
1506:
1500:
1497:
1490:
1486:
1480:
1476:
1465:
1461:
1457:
1451:
1447:
1441:
1438:
1410:
1406:
1403:
1393:
1389:
1381:
1377:
1372:
1364:
1360:
1354:
1350:
1339:
1335:
1331:
1325:
1321:
1315:
1312:
1273:
1270:
1267:
1260:
1256:
1250:
1246:
1240:
1237:
1232:
1228:
1199:
1196:
1192:
1186:
1182:
1178:
1175:
1149:
1145:
1139:
1135:
1129:
1124:
1121:
1117:
1094:
1090:
1064:
1060:
1037:
1033:
1029:
1024:
1020:
1007:
1004:
990:
970:
948:
945:
931:
930:Specific range
928:
925:
924:
915:
913:
902:
899:
894:
891:
882:
878:
870:
866:
861:
857:
854:
851:
846:
843:
838:
831:
827:
819:
815:
810:
806:
803:
800:
794:
791:
786:
783:
773:
769:
761:
757:
752:
748:
745:
718:
714:
691:
687:
664:
660:
637:
633:
607:
604:
599:
596:
588:
585:
580:
577:
571:
568:
563:
560:
537:
517:
512:
509:
504:
501:
494:
491:
486:
483:
476:
473:
468:
465:
458:
452:
449:
444:
441:
418:
396:
390:
387:
382:
379:
373:
370:
364:
361:
354:
350:
346:
340:
320:
298:
294:
271:
267:
246:
241:
237:
233:
228:
224:
220:
217:
197:
177:
164:
161:
88:
87:
42:
40:
33:
26:
9:
6:
4:
3:
2:
5094:
5083:
5080:
5078:
5075:
5074:
5072:
5063:
5061:
5057:
5056:
5051:
5050:
5047:
5044:
5041:
5040:9789065622044
5037:
5033:
5029:
5027:
5025:
5020:
5017:
5015:
5010:
5007:
5006:9780071626965
5003:
4999:
4995:
4991:
4987:
4986:
4973:
4969:
4965:
4964:
4956:
4945:
4941:
4934:
4927:
4919:
4917:9780850451634
4913:
4909:
4902:
4898:
4888:
4885:
4883:
4879:
4878:Fuel fraction
4876:
4874:
4871:
4869:
4866:
4864:
4861:
4859:
4856:
4854:
4851:
4849:
4846:
4844:
4841:
4839:
4838:Flight length
4836:
4835:
4829:
4820:
4807:
4798:
4788:
4778:
4774:
4765:
4755:
4753:
4731:
4721:
4700:
4690:
4684:
4675:
4666:
4661:
4645:
4642:
4639:
4628:
4624:
4618:
4612:
4609:
4606:
4595:
4591:
4588:
4585:
4582:
4579:
4573:
4564:
4555:
4553:
4549:
4548:True AirSpeed
4545:
4527:
4524:
4521:
4517:
4507:
4488:
4478:
4468:
4458:
4452:
4448:
4444:
4441:
4433:
4419:2376 nmi
4416:
4411:
4408:
4394:
4386:
4379:
4376:
4362:
4355:
4352:
4348:
4344:
4341:
4338:
4335:
4331:
4323:
4316:
4313:
4299:
4292:
4289:
4285:
4281:
4278:
4275:
4268:
4261:
4258:
4249:
4242:
4239:
4230:
4227:
4224:
4215:
4205:
4203:
4199:
4196:for kerosene
4181:
4177:
4168:
4163:
4144:
4134:
4124:
4118:
4114:
4110:
4107:
4078:
4053:
4046:
4043:
4034:
4027:
4024:
4015:
4012:
4005:
3985:
3960:
3956:
3950:
3946:
3936:
3916:
3907:
3903:
3882:
3875:
3872:
3865:
3860:
3856:
3850:
3847:
3837:
3834:
3816:
3812:
3804:
3803:
3802:
3784:
3777:
3774:
3765:
3758:
3755:
3746:
3743:
3736:
3732:
3726:
3722:
3711:
3704:
3701:
3694:
3689:
3685:
3679:
3676:
3668:
3664:
3660:
3657:
3649:
3647:
3643:
3638:
3621:
3614:
3611:
3602:
3595:
3592:
3583:
3580:
3573:
3569:
3563:
3559:
3548:
3541:
3538:
3531:
3526:
3523:
3517:
3514:
3505:
3502:
3497:
3481:
3478:
3468:
3464:
3458:
3454:
3446:
3439:
3436:
3429:
3426:
3401:
3397:
3394:
3391:
3385:
3382:
3371:
3351:
3327:
3324:
3314:
3309:
3307:
3303:
3299:
3295:
3290:
3285:
3272:
3265:
3261:
3255:
3251:
3243:
3239:
3235:
3232:
3227:
3223:
3219:
3216:
3202:
3200:
3196:
3176:
3172:
3166:
3162:
3156:
3153:
3146:
3142:
3136:
3132:
3121:
3117:
3113:
3108:
3105:
3099:
3096:
3087:
3085:
3067:
3063:
3040:
3036:
3013:
3009:
3005:
3000:
2996:
2992:
2987:
2983:
2958:
2954:
2948:
2944:
2938:
2935:
2915:
2912:
2909:
2905:
2901:
2898:
2895:
2869:
2865:
2857: ; here
2842:
2837:
2833:
2827:
2824:
2817:
2814:
2792:
2788:
2785:
2775:
2771:
2763:
2759:
2754:
2746:
2742:
2736:
2732:
2721:
2717:
2713:
2708:
2705:
2699:
2696:
2688:
2672:
2652:
2632:
2629:
2626:
2623:
2615:
2611:
2607:
2597:
2582:
2574:
2570:
2564:
2557:
2553:
2546:
2537:
2534:
2531:
2527:
2518:
2513:
2509:
2503:
2499:
2487:
2483:
2479:
2474:
2471:
2463:
2458:
2444:
2424:
2421:
2418:
2412:
2408:
2399:
2395:
2387:
2383:
2378:
2369:
2366:
2363:
2359:
2350:
2345:
2341:
2335:
2331:
2319:
2315:
2311:
2306:
2303:
2283:
2275:
2274:
2268:
2250:
2247:
2244:
2240:
2231:
2226:
2222:
2216:
2212:
2200:
2196:
2192:
2187:
2182:
2179:
2169:
2165:
2149:
2129:
2126:
2121:
2117:
2113:
2108:
2104:
2100:
2095:
2092:
2082:
2077:
2064:
2057:
2053:
2047:
2043:
2035:
2031:
2027:
2024:
2019:
2015:
2011:
2008:
2000:
1998:
1994:
1989:
1987:
1971:
1968:
1961:
1957:
1951:
1947:
1941:
1938:
1935:
1932:
1924:
1921:is used. The
1908:
1901:
1897:
1891:
1887:
1881:
1878:
1870:
1867:The range of
1860:
1839:
1833:
1822:
1800:
1796:
1792:
1766:
1743:
1739:
1710:
1700:
1692:
1689:
1678:
1672:
1669:
1662:
1658:
1654:
1651:
1626:
1621:
1611:
1596:
1580:
1577:
1573:
1569:
1566:
1560:
1557:
1554:
1551:
1548:
1542:
1538:
1534:
1528:
1525:
1518:
1514:
1508:
1504:
1498:
1495:
1488:
1484:
1478:
1474:
1463:
1459:
1455:
1449:
1445:
1439:
1436:
1428:
1425:To obtain an
1423:
1408:
1404:
1401:
1391:
1387:
1379:
1375:
1370:
1362:
1358:
1352:
1348:
1337:
1333:
1329:
1323:
1319:
1313:
1310:
1301:
1299:
1295:
1291:
1287:
1271:
1268:
1265:
1258:
1254:
1248:
1244:
1238:
1235:
1230:
1226:
1217:
1212:
1197:
1194:
1190:
1184:
1180:
1176:
1173:
1164:
1147:
1143:
1137:
1133:
1127:
1122:
1119:
1115:
1092:
1088:
1080:
1062:
1058:
1035:
1031:
1027:
1022:
1018:
1003:
988:
968:
946:
943:
923:
916:
914:
900:
897:
892:
889:
880:
876:
868:
864:
859:
855:
852:
849:
844:
841:
836:
829:
825:
817:
813:
808:
804:
801:
798:
792:
789:
784:
781:
771:
767:
759:
755:
750:
746:
743:
736:
735:
732:
716:
712:
689:
685:
662:
658:
635:
631:
621:
605:
602:
597:
594:
586:
583:
578:
575:
569:
566:
561:
558:
535:
515:
510:
507:
502:
499:
492:
489:
484:
481:
474:
471:
466:
463:
456:
450:
447:
442:
439:
416:
407:
394:
388:
385:
380:
377:
371:
368:
362:
359:
352:
348:
344:
338:
318:
296:
292:
269:
265:
244:
239:
235:
231:
226:
222:
218:
215:
195:
175:
160:
158:
157:
156:Combat radius
152:
150:
146:
142:
138:
134:
132:
128:
124:
123:aviation fuel
120:
116:
112:
108:
104:
94:
84:
81:
73:
63:
59:
53:
52:
46:
41:
32:
31:
19:
5060:MIT turbines
5058:
5054:
5048:
5031:
5023:
5013:
4989:
4972:the original
4962:
4955:
4939:
4926:
4907:
4901:
4826:
4756:
4722:
4662:
4556:
4508:
4429:
4414:
4409:
4206:
4164:
4099:
3650:
3639:
3506:
3498:
3372:
3310:
3286:
3208:
3194:
3088:
2606:stratosphere
2603:
2459:
2271:
2269:
2166:, and S the
2078:
2001:
1990:
1985:
1869:jet aircraft
1866:
1602:
1424:
1302:
1293:
1289:
1285:
1213:
1165:
1009:
933:
917:
622:
408:
331:is equal to
166:
154:
153:
145:ferry flying
140:
139:
135:
131:ground speed
102:
100:
76:
67:
48:
5077:Aeronautics
4544:GroundSpeed
3646:aeronautics
2614:Mach number
2164:air density
2083:equation,
141:Ferry range
62:introducing
18:Ferry range
5071:Categories
4893:References
4882:Mass ratio
3499:Here, the
2079:Using the
163:Derivation
70:April 2023
45:references
4808:⋯
4799:η
4789:η
4779:η
4766:η
4732:η
4676:η
4589:−
4565:η
4518:η
4489:η
4479:η
4469:η
4459:η
4380:^
4356:−
4345:
4339:−
4317:^
4282:
4262:^
4243:^
4231:
4216:η
4145:η
4135:η
4125:η
4079:η
4047:^
4028:^
4016:
3986:η
3917:η
3876:^
3778:^
3759:^
3747:
3705:^
3615:^
3596:^
3584:
3542:^
3482:^
3440:^
3386:^
3328:^
3308:systems.
3302:bleed air
3157:
2936:γ
2896:γ
2755:∫
2565:−
2535:ρ
2379:∫
2367:ρ
2245:ρ
2168:wing area
2150:ρ
2101:ρ
1767:η
1744:∗
1679:η
1663:∗
1499:
1446:η
1371:∫
1320:η
1144:η
1059:η
934:The term
860:∫
837:−
809:∫
751:∫
579:−
503:−
372:−
339:−
5000:(eBook)
4944:Archived
4832:See also
4823:Practice
4552:HeadWind
4198:jet fuel
3304:powered
961:, where
107:aircraft
5008:(print)
3831:is the
3801:where
2162:is the
1827:battery
1705:battery
1616:battery
115:landing
111:takeoff
58:improve
5062:, 2002
5038:
5004:
4996:
4914:
4705:actual
4546:(GS),
3300:, and
2807:where
2645:where
2142:where
1923:thrust
1731:where
528:where
257:where
47:, but
4947:(PDF)
4936:(PDF)
4783:route
4680:route
4483:struc
4220:struc
4149:struc
4083:struc
2437:here
1984:here
1844:total
1771:total
1715:total
1683:total
1631:total
1284:here
103:range
5036:ISBN
5002:ISBN
4994:ISBN
4912:ISBN
4803:temp
4793:wind
4736:temp
4569:wind
4473:aero
4368:fuel
4305:fuel
4139:aero
3990:aero
3055:and
2975:and
2685:the
2081:lift
1997:drag
1077:and
704:and
650:and
208:is:
149:fuel
113:and
4940:DLR
4770:ops
4633:avg
4600:avg
4493:ops
4463:eng
4417:= (
4204:.
4129:eng
3921:eng
3406:acc
3356:acc
3089:Or
3028:).
2916:1.4
1296:is
429:is
5073::
4942:.
4938:.
4880:,
4695:GC
4342:ln
4279:ln
4228:ln
4013:ln
3908:)
3744:ln
3648:.
3581:ln
3370:.
3296:,
3201:.
3154:ln
1496:ln
1286:Wg
1218::
117:.
5042:.
5016:.
4920:.
4775:=
4701:D
4691:D
4685:=
4646:S
4643:A
4640:T
4629:S
4625:G
4619:=
4613:S
4610:A
4607:T
4596:W
4592:H
4586:S
4583:A
4580:T
4574:=
4528:s
4525:p
4522:o
4453:f
4449:Z
4445:=
4442:R
4415:R
4395:)
4387:1
4377:W
4363:W
4353:1
4349:(
4336:=
4332:)
4324:2
4314:W
4300:W
4293:+
4290:1
4286:(
4276:=
4269:2
4259:W
4250:1
4240:W
4225:=
4182:f
4178:Z
4119:f
4115:Z
4111:=
4108:R
4054:2
4044:W
4035:1
4025:W
3961:D
3957:C
3951:L
3947:C
3904:(
3883:T
3873:c
3866:g
3861:f
3857:Z
3851:M
3848:a
3817:f
3813:Z
3785:2
3775:W
3766:1
3756:W
3737:D
3733:C
3727:L
3723:C
3712:T
3702:c
3695:g
3690:f
3686:Z
3680:M
3677:a
3669:f
3665:Z
3661:=
3658:R
3622:2
3612:W
3603:1
3593:W
3574:D
3570:C
3564:L
3560:C
3549:T
3539:c
3532:g
3527:M
3524:a
3518:=
3515:R
3479:W
3469:L
3465:C
3459:D
3455:C
3447:T
3437:c
3430:=
3427:F
3402:W
3398:+
3395:W
3392:=
3383:W
3352:W
3325:W
3273:W
3266:L
3262:C
3256:D
3252:C
3244:T
3240:c
3236:=
3233:T
3228:T
3224:c
3220:=
3217:F
3177:2
3173:W
3167:1
3163:W
3147:D
3143:C
3137:L
3133:C
3122:T
3118:c
3114:g
3109:M
3106:a
3100:=
3097:R
3068:v
3064:c
3041:p
3037:c
3014:s
3010:R
3006:+
3001:v
2997:c
2993:=
2988:p
2984:c
2959:v
2955:c
2949:p
2945:c
2939:=
2913:=
2910:5
2906:/
2902:7
2899:=
2870:s
2866:R
2843:T
2838:s
2834:R
2828:5
2825:7
2818:=
2815:a
2793:W
2789:W
2786:d
2776:1
2772:W
2764:2
2760:W
2747:D
2743:C
2737:L
2733:C
2722:T
2718:c
2714:g
2709:M
2706:a
2700:=
2697:R
2673:a
2653:M
2633:M
2630:a
2627:=
2624:V
2583:)
2575:2
2571:W
2558:1
2554:W
2547:(
2538:S
2532:g
2528:2
2519:2
2514:D
2510:C
2504:L
2500:C
2488:T
2484:c
2480:2
2475:=
2472:R
2445:W
2425:;
2422:W
2419:d
2413:W
2409:1
2400:1
2396:W
2388:2
2384:W
2370:S
2364:g
2360:2
2351:2
2346:D
2342:C
2336:L
2332:C
2320:T
2316:c
2312:1
2307:=
2304:R
2284:W
2273:1
2251:W
2248:S
2241:2
2232:2
2227:D
2223:C
2217:L
2213:C
2201:T
2197:c
2193:1
2188:=
2183:F
2180:V
2130:W
2127:=
2122:L
2118:C
2114:S
2109:2
2105:V
2096:2
2093:1
2065:W
2058:L
2054:C
2048:D
2044:C
2036:T
2032:c
2028:=
2025:T
2020:T
2016:c
2012:=
2009:F
1986:W
1972:;
1969:W
1962:L
1958:C
1952:D
1948:C
1942:=
1939:D
1936:=
1933:T
1909:W
1902:L
1898:C
1892:D
1888:C
1882:=
1879:D
1840:W
1834:/
1823:W
1801:D
1797:/
1793:L
1740:E
1711:W
1701:W
1693:D
1690:L
1673:g
1670:1
1659:E
1655:=
1652:R
1627:W
1622:/
1612:W
1584:)
1581:f
1578:W
1574:/
1570:i
1567:W
1564:(
1561:n
1558:L
1555:p
1552:s
1549:I
1546:)
1543:D
1539:/
1535:L
1532:(
1529:V
1526:=
1519:2
1515:W
1509:1
1505:W
1489:D
1485:C
1479:L
1475:C
1464:p
1460:c
1456:g
1450:j
1440:=
1437:R
1409:W
1405:W
1402:d
1392:1
1388:W
1380:2
1376:W
1363:D
1359:C
1353:L
1349:C
1338:p
1334:c
1330:g
1324:j
1314:=
1311:R
1294:g
1290:W
1272:;
1269:g
1266:W
1259:L
1255:C
1249:D
1245:C
1239:V
1236:=
1231:a
1227:P
1198:r
1195:b
1191:P
1185:p
1181:c
1177:=
1174:F
1148:j
1138:a
1134:P
1128:=
1123:r
1120:b
1116:P
1093:p
1089:c
1063:j
1036:r
1032:P
1028:=
1023:a
1019:P
989:F
969:V
947:F
944:V
922:)
920:1
918:(
901:W
898:d
893:F
890:V
881:1
877:W
869:2
865:W
856:=
853:W
850:d
845:F
842:V
830:2
826:W
818:1
814:W
805:=
802:t
799:d
793:t
790:d
785:R
782:d
772:2
768:t
760:1
756:t
747:=
744:R
717:2
713:W
690:1
686:W
663:2
659:t
636:1
632:t
606:t
603:d
598:W
595:d
587:F
584:V
576:=
570:t
567:d
562:R
559:d
536:V
516:,
511:V
508:F
500:=
493:t
490:d
485:R
482:d
475:t
472:d
467:W
464:d
457:=
451:R
448:d
443:W
440:d
417:R
395:.
389:t
386:d
381:W
378:d
369:=
363:t
360:d
353:f
349:W
345:d
319:F
297:f
293:W
270:0
266:W
245:,
240:f
236:W
232:+
227:0
223:W
219:=
216:W
196:t
176:W
83:)
77:(
72:)
68:(
54:.
20:)
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