Acceleration & Speed

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Suppose we could fly in a plane or could teleport as fast as we wanted. How long would it take us to get anyplace on Earth using a constant acceleration & what would our maximum speed be?

Since it is about 24,000 miles around the Earth, the farthest point away is about 12,000 miles. No matter how far we want to go, we would need to accelerate for the first half of the time, then decelerate for the last half of the time to be able to stop at our destination. So to get 12,000 miles we would have to accelerate for 6,000 miles, then decelerate for the next 6,000 miles. Note that if we wanted to feel like we are always accelerating, we would face forward for the first half & then face backward the last half.

From what I can gather on the Internet it seems that 4 Gs is significantly uncomfortable. When we fly on a commercial aircraft, there is a little less than 2 Gs on takeoff. From the picture we can see that we can go 6,000 miles in slightly less than 15 minutes at 2.5 Gs.

If we accelerate at 2.5 Gs for 15 minutes, how fast will we be going?

One G is about 32.2 ( actually 32.17404856...) feet/second, so 2.5 Gs is about 96.6 feet/second. The graph indicates that we will be going about 822 miles/minute. If we multiply by 60, we get over 49,000 miles/hour. Note that if we kept that maximum speed, we'd go around the Earth more than twice/hour.


When (NOT if) we develop teleportation abilities or a plane or other device that will take us that fast, there are two problems we should address. One is to make sure we don't hit some other plane or teleporting person. The other is the sonic boom.  Sonic booms occur when we go thru the air at more than the speed of sound, which is  768 miles/hour at 68 degrees F in dry air. If we can teleport ourselves, then we probably could teleport air so that we make a tunnel of  no air. Note that if we just move air out of the way near us, the movement of the air still creates a sonic boom. The simplest solution would be to make a tube of no air from start to destination. We could gently move the air out of the way in a second, travel thru it in 30 minutes, then gently let the air back into the tube. A slightly more complicated method would be to make several tubes one after another as we needed them, but still opening & closing them gently. Perhaps we would need an air traffic computer controller to prevent collisions.


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