Only partly joking. Each item is correct. Higher is better. Less air is better. Equatorial is better.
With Earth's radius of 6,000 km, and orbits of 1,414km, another 4 km altitude at launch is not a lot, I admit. But it's better than a poke in the eye with a burnt stick.
Say the weight at launch is 3,000,000 kg at sea level for a Saturn V. en.wikipedia.org
At 4 km altitude at launch, it would weigh only 2,996,000 kg. That's 4,000 kg lighter. 4 tons is a bit of a load for me to lift. Though I agree that 0.1% saving in load doesn't seem like a big deal.
If it was being lifted only 1 km, a 4 km head start would be a big deal, but I admit that even with significant gravity reduction as it goes up, a 1414 km journey up to Globalstar's orbit would mean only a small amount of fuel saved.
Regarding equatorial launches - here are some calculations to save me the trouble. Admittedly, now that I look, Mexico City is not much further south than the South of Florida, so again, it's a trivial gain, but it all helps: <How big is the boost from an equatorial launch? To make a rough estimate, we can determine Earth's circumference by multiplying its diameter by pi (3.1416). The diameter of Earth is approximately 7,926 miles (12,753 km). Multiplying by pi yields a circumference of something like 24,900 miles (40,065 km). To travel around that circumference in 24 hours, a point on Earth's surface has to move at 1,038 mph (1,669 kph). A launch from Cape Canaveral, Florida, doesn't get as big a boost from Earth's rotational speed. The Kennedy Space Center's Launch Complex 39-A, one of its launch facilities, is located at 28 degrees 36 minutes 29.7014 seconds north latitude. The Earth's rotational speed there is about 894 mph (1,440 kph). The difference in Earth's surface speed between the equator and Kennedy Space Center, then, is about 144 mph (229 kph). (Note: The Earth is actually oblate -- fatter around the middle -- not a perfect sphere. For that reason, our estimate of Earth's circumference is a little small.)
Considering that rockets can go thousands of miles per hour, you may wonder why a difference of only 144 mph would even matter. The answer is that rockets, together with their fuel and their payloads, are very heavy. For example, the February 11, 2000 lift-off of the Space Shuttle Endeavor with the Shuttle Radar Topography Mission required launching a total weight of 4,520,415 pounds (2,050,447 kg). It takes a huge amount of energy to accelerate such a mass to 144 mph, and therefore a significant amount of fuel. Launching from the equator makes a real difference. >
But check out the reduced air resistance! Air density reduces a LOT faster with altitude than gravity does. At sea level, there's lots of the stuff getting in the way. At 50km it's hard to breathe. It's not even easy to breathe at 10 km altitude. At lift-off, there's not a lot of drag because it's traveling so slowly, but look how fast it gets going with drag being the square of the speed. The calculation is more tricky, so I won't bother doing it.
4 km out of 40km of air is quite a bit of the stuff to push aside. I can't find rocket speeds at 4km altitude, but I guess they are getting along pretty quickly and the drag is significant. Air pressure is halved at 4km vs sea level so at that altitude, the rocket has already got through half the air.
Okay, I admit I can't make even a slight case for moving launching from Cape Canaveral to Mexico City, even if the Mexicans would let them do it for no cost. Also, I admit did actually think the saving would be a bit more than it would be.
But at least 747s save a lot of fuel getting up to 10km cruise altitude. But hmmmm, on reflection, they wouldn't be able to take off with a big load so they'd earn less money so they'd be better off to take off at lower altitude loaded up with passengers and freight. Damn!! Surely Mexico City is good for something.
Mqurice |
