Has anybody tried computing travel time from Mars?

[tkzv]

There was a thread where someone computed that UFOs need about 1 month to reach Earth from Mars. I can't find it. I tried to calculate the time and got much faster trip.

Does the original game mention the maximum accelerations of UFOs anywhere? I don't think it does.

Let's assume top speed of UFOs is given for lower atmosphere when air friction equals the force of their drives, shall we? In the vanilla a Battleship's speed is 5000 km/h. I tried running a CFD simulation, but ran into problems with ParMGridGen. Let's simply assume that it is a cylinder 25 m in diameter and 9 m tall, about as aerodynamic at supersonic speeds as a sphere (drag coefficient Cd ~1). Drag force at top speed will be 1/2 * 1.3 kg/m^3 * (1400 m/s)^2 * 1 * 225 m^2 ~ 3*10^8 N That's the force its engines can give. If the speed is capped by some other factor, like heat, this means even more powerful engines.

How heavy are battleships? Let's assume about as heavy as Earth aluminium military hovercraft of equal size. I found only craft twice smaller at 100 metric tons and twice larger at 500-600 tons. Let's say 200-300 tons.

This gives maximum acceleration in space up to 300 000 000 / 200 000 = 1500 m/s^2 or 153 g.

Here's a good question: how will the crew and fragile machinery survive this acceleration? I suppose that aliens can maintain comfortable artificial gravitation of ~0.5 g inside their vessels. Either that, or gravity engines make the ship fall free at 150 g, thus nobody inside is hurt.

What is the travel time from Mars to Earth? Minimum distance from Mars to Earth is about 230 - 150 = 80 million km. Maximum distance is 230 + 150 = 380 million km plus some unspecified amount to avoid passing too close to Sun. The shortest trip would take sqrt( 2 * 8*10^10 m / 1500 m/s^2 ) = 10328 s or less than 3 hours.

It is safe to ignore relativistic effects since the speed would not exceed 10 000 s / 2 * 1500 m/s^2 = 7 500 000 m/s or 0.025c.

For longer distance the time and top speed will increase as square root of the distance — still hours and several percent of c.

Any mistakes?

[The Reaver of Darkness]

I'm guessing they don't carry that much fuel. The length of time it takes could be highly dependent on their willingness to reach high travel speed. As you have shown, they can accelerate very fast very quickly. I think they could make the trip in under a day, but they might take a week if they want to be fuel conscious. Whatever the standard time frame is, it's something that can easily be set by the writers, as there are many reasonable values here.

[tarkalak]

If you assume that the UFOs are a tourchship then the path that you take between mars and the earth should be a Brachistotrone curve and not a stright line. Traveling in space isn't just about the distance, you must match the speed and orbit of the target.

A tourchship a ship that is immensely powerful (compared to to today) and runs it's engines at constant acceleration the whole trip.

https://en.wikipedia.org/wiki/Brachistochrone_curve

[The Reaver of Darkness]

If you assume that the UFOs are a tourchship then the path that you take between mars and the earth should be a Brachistotrone curve and not a stright line. Traveling in space isn't just about the distance, you must match the speed and orbit of the target.

At the speeds it'll be traveling, with acceleration many times greater than Earth's surface gravity, its ideal path would be slightly curved yet almost a straight line. They would essentially compute the length of time it takes to reach the destination, and aim ahead of the target based on the movement of the target over that time.

[tarkalak]

At the speeds it'll be traveling, with acceleration many times greater than Earth's surface gravity, its ideal path would be slightly curved yet almost a straight line. They would essentially compute the length of time it takes to reach the destination, and aim ahead of the target based on the movement of the target over that time.

Mars is moving at some orbital speed and Earth is moving at another. The difference will be the dV (delta V, change of velosity) that the UFO needs to do. Like two cars speeding on a circular high way, the UFO is a roller scater that jumps off one car and travels to the other.

A space craft leaving Mars orbit will initially orbit the sun at the same speed Mars is moving and will need to make a burn that changes it's orbit to one that brings it close to Earth and then do another burn to mach its orbit around the Sun(and the ships speed) with Earth.

Calculating the path as if the craft is stationary and only needs to move from point A to B is not accurate. If the UFO just aims at Earth they will collide at a huge speed, most likely destroying the UFO. For a successful randezvous the UFO has to travel to the target and mach speed with it.

[Yankes]

Mars is moving at some orbital speed and Earth is moving at another. The difference will be the dV (delta V, change of velosity) that the UFO needs to do. Like two cars speeding on a circular high way, the UFO is a roller scater that jumps off one car and travels to the other.

A space craft leaving Mars orbit will initially orbit the sun at the same speed Mars is moving and will need to make a burn that changes it's orbit to one that brings it close to Earth and then do another burn to mach its orbit around the Sun(and the ships speed) with Earth.

Calculating the path as if the craft is stationary and only needs to move from point A to B is not accurate. If the UFO just aims at Earth they will collide at a huge speed, most likely destroying the UFO. For a successful randezvous the UFO has to travel to the target and mach speed with it.

This is question how much energy UFO have available to maneuvering. Current space crafts have VERY little of this available (after you burn thousands tons of fuel to exit earth). If UFO can on demand enter and leave earth atmosphere then it could fly in "straight" line from mars to earth and decelerate before entering atmosphere.

Interesting fact, ISS kinetic energy is 1/5 of energy released by Hiroshima atomic bomb:  https://en.wikipedia.org/wiki/Joule#Multiples
This mean UFO energy source should have enough energy to destroy whole city.

[Solarius Scorch]

This mean UFO energy source should have enough energy to destroy whole city.

It depends whether all this energy can be released at once.
An instant ramen pack has enough chemical energy to rival hand grenades, but it can't just explode.

[The Reaver of Darkness]

Mars is moving at some orbital speed and Earth is moving at another. The difference will be the dV (delta V, change of velosity) that the UFO needs to do. Like two cars speeding on a circular high way, the UFO is a roller scater that jumps off one car and travels to the other.

At the acceleration these craft can sustain, they would be able to reach orbital velocity in seconds. After a few hours of acceleration, they would be going many times the speed of the planets they're traveling between. It would be more like riding a motorcycle onto the autowalk at the airport.

[Yankes]

It depends whether all this energy can be released at once.
An instant ramen pack has enough chemical energy to rival hand grenades, but it can't just explode.

This is good point to consider, probably similar to nuclear bomb / power plant. Question is to what end UFO is closer to.

[Solarius Scorch]

This is good point to consider, probably similar to nuclear bomb / power plant. Question is to what end UFO is closer to.

I have no solid info here, but I think the big thing about the E-115 is not only energy density, but also fine control of energy release.
If a UFO Power Source could be turned into a big elerium bomb easily, it would lead to some unfortunate consequences. (Such as late game X-Com holding a strategic arsenal comparable with nuclear powers.)