RGClark
Mathematician
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The benefits of air launch go beyond just the speed and altitude attained. This is discussed in this report:
Air Launching Earth-to-Orbit Vehicles: Delta V gains from Launch Conditions and Vehicle Aerodynamics.
Nesrin Sarigul-Klijn University of California, Davis, CA, UNITED STATES; Chris Noel University of California, Davis, CA, UNITED STATES; Marti Sarigul-Klijn University of California, Davis, CA, UNITED STATES
AIAA-2004-872
42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan. 5-8, 2004
http://pdf.aiaa.org/preview/CDReadyMASM04_665/PV2004_872.pdf [first page only]
The conclusions are summarized in this online lecture:
A.4.2.1 Launch Method Analysis (Air Launch).
"For a launch from a carrier aircraft, the aircraft speed will directly reduce the Δv required to attain LEO. However, the majority of the Δv benefit from an air launch results
from the angle of attack of the vehicle during the release of the rocket. An
ideal angle is somewhere of the order of 25° to 30°.
"A study by Klijn et al. concluded that at an altitude of 15250m, a rocket launch with the
carrier vehicle having a zero launch velocity at an angle of attack of 0° to
the horizontal experienced a Δv benefit of approximately 600 m/s while a launch
at a velocity of 340m/s at the same altitude and angle of attack resulted in a
Δv benefit of approximately 900m/s. The zero launch velocity situations can
be used to represent the launch from a balloon as it has no horizontal velocity.
"Furthermore, by increasing the angle of attack of the carrier vehicle to
30° and launching at 340m/s, a Δv gain of approximately 1100m/s
was obtained. Increasing the launch velocity to 681m/s and 1021m/s produced a
Δv gain of 1600m/s and 2000m/s respectively.
"From this comparison, it can be seen that in terms of the Δv gain, an airlaunch is
superior to a ground launch. As the size of the vehicle decreases, this superiority
will have a larger effect due to the increased effective drag on the vehicle."
https://engineering.purdue.edu/AAE/...4.2.1 Launch Method Analysis (Air Launch).doc
A speed of 340 m/s is a little more than Mach 1, while subsonic transport aircraft typically cruise
slightly below Mach 1. So the delta-V saving could still be in the range of 1,000 m/s with air launch,
a significant savings by the rocket equation.
Bob Clark
Air Launching Earth-to-Orbit Vehicles: Delta V gains from Launch Conditions and Vehicle Aerodynamics.
Nesrin Sarigul-Klijn University of California, Davis, CA, UNITED STATES; Chris Noel University of California, Davis, CA, UNITED STATES; Marti Sarigul-Klijn University of California, Davis, CA, UNITED STATES
AIAA-2004-872
42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan. 5-8, 2004
http://pdf.aiaa.org/preview/CDReadyMASM04_665/PV2004_872.pdf [first page only]
The conclusions are summarized in this online lecture:
A.4.2.1 Launch Method Analysis (Air Launch).
"For a launch from a carrier aircraft, the aircraft speed will directly reduce the Δv required to attain LEO. However, the majority of the Δv benefit from an air launch results
from the angle of attack of the vehicle during the release of the rocket. An
ideal angle is somewhere of the order of 25° to 30°.
"A study by Klijn et al. concluded that at an altitude of 15250m, a rocket launch with the
carrier vehicle having a zero launch velocity at an angle of attack of 0° to
the horizontal experienced a Δv benefit of approximately 600 m/s while a launch
at a velocity of 340m/s at the same altitude and angle of attack resulted in a
Δv benefit of approximately 900m/s. The zero launch velocity situations can
be used to represent the launch from a balloon as it has no horizontal velocity.
"Furthermore, by increasing the angle of attack of the carrier vehicle to
30° and launching at 340m/s, a Δv gain of approximately 1100m/s
was obtained. Increasing the launch velocity to 681m/s and 1021m/s produced a
Δv gain of 1600m/s and 2000m/s respectively.
"From this comparison, it can be seen that in terms of the Δv gain, an airlaunch is
superior to a ground launch. As the size of the vehicle decreases, this superiority
will have a larger effect due to the increased effective drag on the vehicle."
https://engineering.purdue.edu/AAE/...4.2.1 Launch Method Analysis (Air Launch).doc
A speed of 340 m/s is a little more than Mach 1, while subsonic transport aircraft typically cruise
slightly below Mach 1. So the delta-V saving could still be in the range of 1,000 m/s with air launch,
a significant savings by the rocket equation.
Bob Clark
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