A friend of mine and I were talking about how, when he was a high school student, he was then riding the wave of new IT breakthroughs which have since become commonplace all over the world - like the internet. Recently he told high school students in Singapore that they are riding the wave of new developments which similarly could become commonplace in the future.
I mentioned that one area in which we have not seen significant improvements in recent decades is travel-time between the continents, especially since the Concorde went out of service.
So I wondered whether the idea of travel in a vacuum tunnel shouldn't be revisited. It certainly would help the causes of world missions, economics and human rights if we could travel to Singapore, New York or London in under a few hours!
The technology already exists to move a physical object that fast. The current land speed record is 10,325km/h using a rocket sled. My friend calculated that you could get to New York in under 3 hours at that speed. Even higher speeds could be achieved with a maglev train in a vacuum tunnel.
But can the human body withstand the g-forces required to accelerate to such speeds if one was to travel from say Brisbane to New York in under a few hours?
If you accelerated at the same rate as the shinkansen (2.4km/h/s) continuously to the halfway point and then began decelerating at the same rate from the halfway point until reaching your destination, the g-force on the body might be bearable, and you'd eventually reach a pretty high peak velocity - but it wouldn't cut enough time off the trip compared to traveling by air, plus it mightn't be all that comfortable a trip if you were accelerating and decelerating the whole time.
So it would be necessary to accelerate much quicker, then hold your peak velocity for longer, followed by a short period of deceleration at the end. But the limiting factor still would be the human body's ability to cope with the g-forces during acceleration and deceleration. My friend responded with the following:
"It's been a while since I've done acceleration calculations but the force of gravity (1G) causes any mass to accelerate at 9.81m/s/s (I'll round it up to 10/m/s/s for simplicity).
After 60s or 1min the velocity would be 600m/s or 36,000m/min or 2,160km/h. Because the acceleration is constant, after 2min the velocity would be 4,320km/h, after 5min the velocity would be 10,800km/h.
So if the body can withstand the force of gravity for 5min then you would be travelling at 10,800km/h. The horizontal force of gravity would just give the same feeling as lying down (whilst sitting upright).
Jetfighters travel at about 2,000km/h and I'm sure they can reach that speed in about 1min so I don't think it is unreasonable. (I just read that a MiG-29 accelerates at 10.43m/s/s: http://answers.yahoo.com/question/index?qid=20090407224519AAMJkR5)
Someone else calculated that an Airbus A380 accelerates at 2.28m/s/s (but also that the acceleration also accelerates!). If that acceleration could be maintained for an hour the final speed would be 8,208km/h (of course at that speed you would be at your destination within an hour!). I have a feeling that the peak acceleration you feel when taking off is actually much higher than the average acceleration reported.
Nonetheless I think 5min is quite reasonable to reach 10,000km/h. The main issue will be the energy used to achieve such acceleration..."
Later my friend tried to work out the energy required to accelerate to 10,000km/h in 5min, and he concluded:
"W = Fd
W is the Work (basically the energy) required to apply a force F over a distance d.
F = ma (i.e. mass x acceleration)
Let's say we want to move 100 people all weighing 100Kg (10,000Kg total) at 10m/s/s then the constant force required would be 100,000N.
Now over what distance do we need this force to apply? That's slightly complicated because we aren't travelling at a constant speed whilst accelerating.
It takes 5min (or 300s) to reach 10,000km/h.
The distance travelled equation is:
s = a x t x t / 2
s = 10 x 300 x 300 / 2
s = 45,000m (45km)
Going back to the work equation:
W = Fd
W = 100,000 x 45,000
W = 4500MJ (mega joules)
I think if we divide the Joules by time we get Watts (although I'm not sure whether it is constant): 4,500,000,000J / 300s = 15MW.
Even though that may sound like a lot, my recent power bill showed I used 276kWh in the last quarter. And my power usage is quite low (household of one, no TV, etc.). 276kWh = 993MJ. My bill was $99.87. So basically it would only cost 4.5 times that for the acceleration component of the trip (about $450) in energy.
Of course with all these calculations I could've made a mistake somewhere! I also didn't take into account the weight of the vehicle itself and any fuel it is carrying. I think the lightest and cheapest solution would be to power it by electricity. I also didn't take into account any resistance such as friction."
And he added:
"Flight distance from Brisbane to Singapore: 6,155km.
It would take about 37min to get there plus about 10min total in the acceleration and deceleration components. That's quicker than catching the train to Brisbane airport."
I suppose the main question I still have is concerning the typical passengers' ability to cope with experiencing 1g force. Transporting freight wouldn't have the same restrictions, depending on what the freight was.
Nevertheless, let's hope something will happen to speed-up travel-time, for the sake of God's work, if God wills.
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