Yes, just to add, you can do this however in an evacuated tunnel. Then there is no limit due to friction. Better to use maglev rather than wheels when you get to the orbital velocity 7.9 km / second at ground level, which is much faster than even a hypervelocity bullet - so no contact with the walls of the tunnel.
Anyway at that speed you would be in zero g inside your car. And you can go even faster, if you go faster then you experience artificial gravity pushing you towards the roof of your "car". So you'll be upside down with your head towards the ground.
BTW I have done all these equations in a form which lets you copy / paste them into Google to use it as a calculator.
The acceleration is v^2/r. So to get a particular acceleration you have v = sqrt(a*r). With gravity, then r = 6,371,000 meters and a = 9.8 m / sec^2 then sqrt(6,371,000*9.8) =7900 meters per second.
So, with circumference of the Earth as 2*PI*6,371 km, then that makes it PI*6,371/(60*7.9) minutes to get to the far side of the Earth, or about 42 minutes.
If you accelerate faster, enough to have a comfortable 1 g of artificial gravity, then that becomes sqrt(6,371,000*2*9.8) or 11.175 km / second PI*6,371/(60* 11.175) or 29.85 minutes.
So - in principle you could get to the other side of the Earth in just under 30 minutes. But that's not allowing for time needed to accelerate and decelerate .
If you accelerate at 9.8 m / sec^2 - which takes you over full gravity combined with the force downwards due to gravity, but easily tolerable - then it takes 7900/(60*9.8) or 13.44 minutes to get up to the point where you are in zero g.
For the faster journey it's 11175/(60*9.8) or 19 minutes to get up to the point where you feel full gravity away from the Earth. So in practice y ou'd spend all the time accelerating and decelerating.
Using [math]s =0.5* a*t^2[/math] then after 19 minutes accelerating at 1 g then the distance traveled is 0.5*9.8*(19*60)^2 or 6,368 km. So with 19 minutes at start and end of your journey, the distance left is PI*6,371-2* 6,368 or 7279 km which at 11175 meters per second you can travel in 7279000/(11175*60) or 10.86 minutes.
So, if we could build a MagLev train that goes all the way around the Earth in an evacuated tunnel, traveling faster than a bullet - you can get to the other side of the Earth comfortably in about 49 minutes, going up to sqrt(2)*g at the start and end of the journey but spending most of the journey at around ordinary levels of gravity. You could reduce this a bit more if you are able to withstand high g forces.
Anyway at that speed you would be in zero g inside your car. And you can go even faster, if you go faster then you experience artificial gravity pushing you towards the roof of your "car". So you'll be upside down with your head towards the ground.
BTW I have done all these equations in a form which lets you copy / paste them into Google to use it as a calculator.
The acceleration is v^2/r. So to get a particular acceleration you have v = sqrt(a*r). With gravity, then r = 6,371,000 meters and a = 9.8 m / sec^2 then sqrt(6,371,000*9.8) =7900 meters per second.
So, with circumference of the Earth as 2*PI*6,371 km, then that makes it PI*6,371/(60*7.9) minutes to get to the far side of the Earth, or about 42 minutes.
If you accelerate faster, enough to have a comfortable 1 g of artificial gravity, then that becomes sqrt(6,371,000*2*9.8) or 11.175 km / second PI*6,371/(60* 11.175) or 29.85 minutes.
So - in principle you could get to the other side of the Earth in just under 30 minutes. But that's not allowing for time needed to accelerate and decelerate .
If you accelerate at 9.8 m / sec^2 - which takes you over full gravity combined with the force downwards due to gravity, but easily tolerable - then it takes 7900/(60*9.8) or 13.44 minutes to get up to the point where you are in zero g.
For the faster journey it's 11175/(60*9.8) or 19 minutes to get up to the point where you feel full gravity away from the Earth. So in practice y ou'd spend all the time accelerating and decelerating.
Using [math]s =0.5* a*t^2[/math] then after 19 minutes accelerating at 1 g then the distance traveled is 0.5*9.8*(19*60)^2 or 6,368 km. So with 19 minutes at start and end of your journey, the distance left is PI*6,371-2* 6,368 or 7279 km which at 11175 meters per second you can travel in 7279000/(11175*60) or 10.86 minutes.
So, if we could build a MagLev train that goes all the way around the Earth in an evacuated tunnel, traveling faster than a bullet - you can get to the other side of the Earth comfortably in about 49 minutes, going up to sqrt(2)*g at the start and end of the journey but spending most of the journey at around ordinary levels of gravity. You could reduce this a bit more if you are able to withstand high g forces.
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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