Calculate hopper deltaV

[Jackissimus]

Hi,

I want to design a craft capable of performing two short hops on the surface of the Mun. The hops would be no more than 40km long, the craft would need refueling afterwards. I have two questions:

1) How do you properly calculate the deltaV for such a craft? I think this page doesn't have the relevant equations.

2) How do you intuitively guesstimate the deltaV for that craft?

I can always use trial and error, but care to make it interesting?

[znode]

Hi,

I want to design a craft capable of performing two short hops on the surface of the Mun. The hops would be no more than 40km long, the craft would need refueling afterwards. I have two questions:

1) How do you properly calculate the deltaV for such a craft? I think this page doesn't have the relevant equations.

2) How do you intuitively guesstimate the deltaV for that craft?

I can always use trial and error, but care to make it interesting?

What you're looking for is a ballistic missile trajectory, since you're looking for the most efficient sub-orbital ellipse that intersects with the ground at an arbitrary ground distance.

Someone was nice enough to scan in the full copy of Bate, Muller, and White. Written by three professors of astronautics of the US Air Force Academy, this is literally the textbook on astrodynamics used by almost everyone everywhere, and contains all the math you'd need to suborbit, orbit, or transfer virtually anything anywhere in system, in real life.

Equations will be on page 277 (pg 292 of the pdf), Chapter 6, ballistic missile trajectories.

[Jackissimus]

What you're looking for is a ballistic missile trajectory, since you're looking for the most efficient sub-orbital ellipse that intersects with the ground at an arbitrary ground distance.

Someone was nice enough to scan in the full copy of Bate, Muller, and White. Written by three professors of astronautics of the US Air Force Academy, this is literally the textbook on astrodynamics used by almost everyone everywhere, and contains all the math you'd need to suborbit, orbit, or transfer virtually anything anywhere in system, in real life.

Equations will be on page 277 (pg 292 of the pdf), Chapter 6, ballistic missile trajectories.

Wow. Exactly what I was looking for, short & long term. Who are you? Just one post? Thanks a million!

[capi3101]

Been too long since I've done force balance equations...fifteen years since engineering physics.

A lot of the specifics are going to depend on what engine you use and the final mass of your craft, as well as your launch angle.

As far as the delta-V requirement goes, though, it should just be four times the amount needed to get the craft up to the proper apoapsis. You need that much to get your horizontal velocity to where it needs to be, then to zero, then to the same amount, then back to zero.

If you launch at 45 degrees along the desired heading, stop your burn when your apoapsis reaches 20,000 + your reference height (i.e. the altitude of your launch site). Note the time to apoapsis when the burn ends. Point your ship at the retrograde marker when you get to the apoapsis and when the time past apoapsis equals the amount of time before apoapsis at which you started your burn, begin your retroburn for landing. That oughta get you close to a safe landing roughly 40k away. That'd be one hop.

Once again, though, the specifics are going to depend on the initial mass of the craft. That'll get you an acceleration figure.

Of course, since your mass is changing, that acceleration won't be constant either...

Edited July 22, 2013 by capi3101