AE 440A Initial Sizing
Due Sept. 11, 2008
Consider a horizontal take-off, air-launch vehicle for the SpaceX Falcon 1 launcher
(www.spacex.com). The Falcon 1, powered by LOX and kerosene is 21.3 m long and
approximately 2m in diameter, with a launch mass of 27,670 kg. The vehicle will carry
Falcon 1 rocket to a launch point, separate, and return to base with a two-person crew
(assume each crew member weighs 90 kg). The design will take off from a runway in
the United States. The launch point of the Falcon rocket from the aircraft is 800 km from
take-off airport (e.g. Cape Canaveral). The vehicle would cruise at subsonic speeds
(Mach 0.85) at an altitude of 30 km to the air-launch (rocket separation) point and the
briefly accelerate to Mach 2 for launch for a distance of 200 km. Assume L/D=12 at
subsonic cruise and an L/D=5 for supersonic conditions. For initial sizing purposes, the
design must account for a launch abort, i.e. assume that payload is not released during
mission. A 1000 km return to the same airport then occurs.
RECOMMENDATION: Use Excel for your plots and calculations as it will make it
easier to change numbers if you make a mistake.
1) 10 points Conduct a historical survey of at least four vehicles (built or in
development) which are relevant to this Falcon-launch vehicle in terms of mission and
capability and discuss the similarities and differences. Estimate (to the best extent
possible) aspect ratio, engine type, maximum take-off weight, and empty weight fraction
of each of these vehicles.
2) 10 points Plot* the empty weight fractions (as symbol points) as a function of
maximum take-off weight. On this same plot, include one or two relevant curves from
Raymer’s Table 3.1. Using the data points from the aircraft in part 1) that are most
reasonable and representative, determine an empirical equation of the empty weight
fraction as a function of take-off weight (i.e. find appropriate A and c values) and put a
trend line based on these values on the same plot. Based on your research in part 1)
determine what type of engine the Falcon-launch vehicle would probably use and the
SFC for the subsonic and supersonic legs based on Fig. 3.3 of Raymer.
3) 10 points Sketch a diagram showing the mission with leg numbers. Conduct an initial
sizing of the Falcon-launch vehicle based on the above information to determine total
aircraft take-off weight (in kg). Show all equations and all work . Don’t forget units and
use significant figures.
4) 10 points a) Conduct a vehicle trade study of a single mission parameter (e.g.
subsonic Mach number, launch Mach number, range, launch altitude, crew number,
payload mass, etc.) and b) an empirical coefficient (e.g. engine SFC, empty weight
fraction, (L/D)max, etc.) to see their influence on total aircraft weight. Use a reasonable
