Packing the Air/Raft

[AnotherDilbert]

(V=A*T^2, since we're not decelerating to a stop after the midpoint.)

constant acceleration:

a = constant [m/s²]

v = a × t [m/s]

d = a × t² / 2 [m]

Just integrate the function over t for each step.



If you check the dimensions in your equation you can see it is not correct:
A*T^2 [m/s² × s × s = m] has the dimension of a distance, it can't be a velocity which has the dimension [m/s].

 

[Grav_Moped]

constant acceleration:

a = constant [m/s²]

v = a × t [m/s]

d = a × t² / 2 [m]

Just integrate the function over t for each step.



If you check the dimensions in your equation you can see it is not correct:
A*T^2 [m/s² × s × s = m] has the dimension of a distance, it can't be a velocity which has the dimension [m/s].

Good catch - thanks!

LEO orbital velocity is 7.8km/sec
=7800m/sec

v=at
v in m/sec, a in m/sec, t in sec

7800m/sec=1m/sec*t
Units cancel.
7800=t
7800 seconds is 130 minutes or 2.167 hours.

So, accelerating at 0.1G (approx. 1m/sec) gets you to 7.8km/sec LEO (low earth orbit) orbital velocity in 130 minutes, if you're starting at 0 velocity and ignoring gravity.

Getting to 1000km LEO altitude takes 1.55 hours (1 hour for the first 30km in the lower atmosphere where it's limited to 30km/hr ascent, 33 minutes for the remaining 970km at T=2*sqrt(D/A) -- above 30km altitude, air density drops off faster than velocity accumulates).

16.5 minutes after the hour-long climb out of the lower atmosphere, the anti-grav gets dialed back to 90% weight cancellation, providing downward acceleration of 0.1G to keep from overshooting the desired altitude. At this time, the 0.1G that was being used to accelerate upward is shifted to lateral acceleration. 16.5 minutes later, the anti-grav is returned to full weight cancellation as the Air/Raft's vertical vector has decreased to zero and it is at the desired altitude.

This lateral acceleration, as noted above, takes a little over two hours to achieve orbital velocity (of which 16.5 minutes were spent coasting upward).

Total time to orbital altitude and velocity is a little under three and a half hours.

However, this is just "get into AN orbit," not a specific orbit, let alone making a rendezvous with something in that specific orbit. If attempting to rendezvous with something in orbit, the Air/Raft will need to position itself directly under the target's orbital track (which may take a while) and wait up to an hour and a half (and longer for higher orbits) for the target to be at the correct position in its orbit (so the Air/Raft doesn't have to either let it catch up or have to chase it down).

 

[AnotherDilbert]

v in m/sec, a in m/sec, t in sec

a in m/s/s = m/s².


Velocity is the change in position per time, hence the dimension is position/time [m/s].

Acceleration is the change in velocity per time, hence the dimension is velocity/time [m/s/s = m/s²].

Sorry, units matter.

7800m/sec=1m/sec*t
Units cancel.
7800=t

The numbers are right, but the units not.

V = 7800 [m/s] = at = 1 [m/s²] × t

Units multiply as usual, both sides of the equation must have the same unit.

So, accelerating at 0.1G (approx. 1m/sec) gets you to 7.8km/sec LEO (low earth orbit) orbital velocity in 130 minutes, if you're starting at 0 velocity and ignoring gravity.

Yes, if you are accelerating in a straight line in free space. Sadly this case is a bit more complicated. We are accelerating in a spiral around the planet, carefully maintaining the correct orbital speed for the current height.

 

[Grav_Moped]

...
The numbers are right, but the units not.

Good catch.

Yes, if you are accelerating in a straight line in free space. Sadly this case is a bit more complicated. We are accelerating in a spiral around the planet, carefully maintaining the correct orbital speed for the current height.

It resolves into "going up" and "going sideways" since centripetal acceleration is effectively free, for amounts up to 1G.

The ascent track (in an external reference frame, not with respect to the planet's surface) isn't a spiral. It's a vertical ascent (wavy at the very bottom due to wind drift), which turns at about halfway up from vertical into a curve that's tangent to the orbital path, then follows the orbital path while accelerating the rest of the way to orbital velocity.

The first 515km of ascent (drag-limited below 30km, of course) is straight up. The next 485km (altitude) are a curve tangent to the vertical and to the 1000km altitude orbit, as the vertical vector decreases from 990m/sec

Spoiler:

990 seconds of 1m/sec acceleration, started at 30km altitude

to zero

Spoiler:

0.1G downward acceleration from cancelling all but 10% of the Air/Raft's weight with antigrav, for 990 seconds

and the horizontal vector increases to 990m/sec

Spoiler:

1m/sec lateral acceleration, which up until then had been used for vertical acceleration.

At this point the Air/Raft is at orbital altitude and following the orbital track, but has only about 1/8 orbital velocity. It will need almost full weight neutralization to maintain this altitude in this condition. However, it's still accelerating and will reach orbital velocity about two hours later. Over the course of those two hours, altitude is kept constant by gradually decreasing the weight neutralization toward zero.

I suppose you could use a "spiral" track. Vertical ascent above atmosphere would then be "accelerate upwards for 139 seconds (to 500km/h), then coast with full weight compensation (no weight) for two hours while accelerating laterally at 0.1G, then kill the vertical vector by turning off the weight compensation for 13.9 seconds".
This would let you start the horizontal acceleration sooner, saving 15 minutes.

Then again, if you're starting to accelerate sideways/up at 100km altitude instead of straight up, the Air/Raft might hit its (air density adjusted) drag limited airspeed before the atmosphere thins out enough with altitude... could knock off a few minutes of the time savings.

 

[Straybow]

Yes, if you are accelerating in a straight line in free space. Sadly this case is a bit more complicated. We are accelerating in a spiral around the planet, carefully maintaining the correct orbital speed for the current height.

That's the point. With a grav vehicle that is entirely unnecessary. The vehicle holds any arbitrary height without regard to orbital mechanics.

 

[kilemall]

Well this wasn't where I was intending this thread to go.



We so nerdy.

 

[Proneutron]

Well this wasn't where I was intending this thread to go.

Here ya go. A/R Storage

 

[kilemall]

Here ya go. A/R Storage

Of COURSE <smacks forehead>!

 

[coliver988]

Here ya go. A/R Storage

Nailed it!:rofl:

 

[BRover]

Here ya go. A/R Storage

It's been improved since. Purse-sized car parking (TL 13?)

 

[Proneutron]

It's been improved since. Purse-sized car parking (TL 13?)

Yep, TL 13 ATV :toast:

 

[Straybow]

We so nerdy.

I have not yet begun to nerd.

 

[Spinward Scout]

I have not yet begun to nerd.

This is why I love this forum.

:coffeesip:

 

[Jame]

The classic air/raft is open topped.


Given it's usual dimensions, couldn't you store it tail-down vertically or bottom/grav modules up against the cargo/vehicle bay wall and fit it into 2 tons?

I'm fully of the opinion that the air/raft is enclosed, just like and for the same reasons as a modern ground car - for example, against bad weather.

Do as you like for YTU, as this is a game we play for fun.

 

[Grav_Moped]

I'm fully of the opinion that the air/raft is enclosed, just like and for the same reasons as a modern ground car - for example, against bad weather.

Do as you like for YTU, as this is a game we play for fun.

The fiction from which the Air/Raft was drawn had them open-topped.

Also, it simplifies determining arcs of fire for PCs and NPCs employing small-arms from within the vehicle.

But yeah, they really ought to be enclosed and pressurized with basic life support for a few hours, or at least have a convertible top by default. Maybe a retractable hardtop?

 

[Proneutron]

I'm fully of the opinion that the air/raft is enclosed, just like and for the same reasons as a modern ground car - for example, against bad weather.

Yes, made that change in '79. The days of the buckboard were long gone.

 

[Condottiere]

I'm thinking pick up truck.

 

[Grav_Moped]

I'm thinking pick up truck.

I went with the art in LBB3, but functionally, it's an anti-grav Deuce-and-a-Half (M35 Series 2 1/2-ton 6x6 cargo truck) [Wikipedia] with a pair of jump seats in the cargo bed to seat 4 including the driver. And Mr. Miller knew Deuce-and-a-halfs.

Layout is probably more like the modern cab-forward equivalents to those trucks.

Personally, I think more in terms of the VW Vanagon (it's so very 1980, and actually has a similar performance envelope aside from the whole "flying" bit -- build it with the huge sunroof and it's effectively open-topped) and its double-cab pickup version. Only slightly larger.

 

[Straybow]

Close, certainly. The deuce-and-a-half would be a bit over 3 dT. A largest rental trucks, 13 ton gvw, would be more like a 4 dT vehicle.

 

[Condottiere]

Would suppose they would be extremely popular as Technicals.