## Energy

Most jet aircraft have an absolute ceiling of 10 miles, or about 50,000 ft, which is about the maximum height to which jet aircraft can climb. High-performance aircraft have certainly exceeded this altitude, but ascending much above 70,000 ft

 Airplanes Rocketships Spaceplanes Operating altitude 10 miles Unlimited Unlimited Operating speed Mach 0.8 Mach 35 Mach 35 Specific energy (ft2/s2) 2 million 650 million 650 million Reusable Yes No Yes Refuelable Yes No Yes Economical Yes No Yes Affordable Yes No Yes Safe Yes No Yes One-piece design Yes No Yes Simple operations Yes No Yes Good infrastructure Yes No Yes

requires advanced propulsion. Spacecraft and rockets are specifically designed to reach extreme altitudes, giving them a much higher potential energy than a typical airplane. Physicists normally include the mass of an object in calculations of both potential and kinetic energies, but to compare objects - or vehicles - of unequal sizes or weights, it is convenient to divide the mass out of the equation, which yields a quantity called specific energy. This is simply the energy per unit mass of the body, and includes both the potential and kinetic energies. From these considerations, it is plain to see that any orbital or interplanetary spaceship would possess a much higher specific energy than any airplane in flight, because of the great altitudes and speeds at which it travels. At 52,800 ft, an airplane has a specific potential energy of 1.70, given in units of million feet squared per second squared. We will use these units for all of our specific energy comparisons. Spacecraft operating at altitudes of at least 100 km, or 62 miles, have specific potential energies of at least 10.6, which is 6.2 times higher than those of airplanes flying at 10 miles.

The airplane is assigned a speed of Mach 0.8, or about 600 mph, which again is typical of modern jet transports. High-performance aircraft routinely exceed this speed. Yet they never begin to approach the Earth-orbital speed of Mach 25. Rocket-powered spaceships, on the other hand, are capable of speeds greater than 25,000 mph, required to escape from Earth's gravity completely. Clearly, there is a huge disparity between the speeds of airplanes and those of rocketships. As in the case of potential energy, rockets command very high kinetic energies, compared with airplanes, because of their great speeds. An airplane flying at 600 mph, or 880 ft/s, has a specific kinetic energy of 0.387 when compared with a rocket flying at 36,000 ft/s, which has a specific kinetic energy of 648. This is 1,670 times higher.

From the above figures, the total specific energies of 600-mph airplanes and 25,000-mph rockets escaping Earth from a height of 62 miles are, respectively, 2.09 and 659. The rocket's total energy is therefore 315 times higher than the airplane's. This is why spaceflight is so difficult. It involves the harnessing of over 300 times as much energy as airplanes have to harness. On the other hand, airplanes can fly for long periods of time without running out of fuel, and never shut down their engines. Rockets run their engines for mere minutes at a time, and quickly exhaust their entire propellant supply.

I t is also interesting to note the energy distribution of airplanes compared to rockets. For the airplane example given above, the energy is 19% kinetic, and 81% potential, ignoring for the moment the potential energy stored in unburned fuel. For the rocket example, the energy is more than 98% kinetic, and less than 2% potential. As the rocket escapes from Earth's gravity well, it will gradually slow down, converting its energy of speed into energy of altitude. Kinetic energy is thereby gradually converted into potential energy.

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