Designing the Space Gun

[Topaz]

Before I got sick and disappeared for a few weeks, I’d promised to attempt a rough design study of the Martian Cylinder spacecraft and its’ Space Gun launch system. The idea came from all the information I and the other folks on the “Uncontrolled Landing” thread were able to guesstimate about the cylinder and gun. Now I’m back and I’ll try and fulfill that promise.

This is going to be what the aerospace community would call a 'First Order Sizing'. The idea isn't to find absolute answers about everything, but simply to define a rough configuration for further study later. We'll find the boundaries of some design points, and do some quick trade-offs to find the best overall approach, assuming I can find some good parameters to study. I'll put in some of the calculations I'm doing here, so you can see what I'm doing. In reality, the calculations are on an Excel spreadsheet. Once we're done, if anyone wants a copy of the spreadsheet, PM me with your e-mail address and I'll send you a copy. That way you can play with the variables yourself and see what happens.

A couple of things are worth noting: The first is that I'm doing this based on our technology. I'm not designing the actual system the Martians used, since Wells doesn’t give us enough information, but rather a possible system that meets the description and works with known technology. It could be the type of thing the fictional Martians used, or it could be totally off the mark. You decide.

Another thing to note is that I'll be making a lot of assumptions. Some of them will be 'good' and fairly accurate; others will be more of a stretch. That's appropriate for this level of design because coming up with the 'right' answer would involve methods and calculations that I either don't have in the first place, or don't have time to do. I'll try to note the good and bad assumptions as we go along. No doubt many of you will be willing to point out that some of my assumptions are better than others! :-)

[Topaz]

The Cylinder, Part I

I'll start with the cylinder, because it's the characteristics of the cylinder that will largely determine the characteristics of the launch gun.

Wells gives us only one pertinent number about the cylinder:

Diameter = 30 yards = 90 feet

Obviously we can guess the shape from the fact that he calls it a "cylinder." While I like the dramatic impact of an asteroid-shaped craft, for the sake of simplicity and accuracy to the text I'll assume the basic shape of the vehicle is a right circular cylinder.

The number Wells doesn't give us is the length of the cylinder. From our earlier discussions, I’m going to arbitrarily set this at 270’ for the main cylinder body.

(BTW, this is where methodology comes into play a bit. Normally, one would define the required volume for the Martians and all their equipment, and then design the dimensions of the vehicle around that. Unfortunately, until someone does definitive designs of all of their machines and devices - and how to stow this material in the cylinder - we have no way of knowing those values. So I'm going to do this backwards and set the dimensions of the vehicle up front. If, at the end, we all decide that this leaves an unreasonably small volume for the Martians and their gear, I'll go back and resize the vehicle to accommodate that. Using a spreadsheet makes this fairly easy.)

So, after all that long-winded discussion,

Length = 270 feet

Knowing that the cylinder is circular in cross-section, we get a total volume of:

Volume_cyl = 1,717,666 cubic feet.

Another handy number we’ll need to know for designing the gun would be the overall weight of the cylinder, and here we run into another problem. We don’t know how much any of the Martian equipment weighs, nor do we know yet how much propellant (if any) the system needs for additional boost, course corrections, or landing retrofire (if any), nor even the weight of the basic structure. We have to estimate using things we know.

The only manned interplanetary spacecraft I know about (in detail) is the Apollo Command Module/Service Module combo. The Soviet Zond series did a similar mission (the fact that it was unmanned was Soviet caution in the face of the N1 booster continually exploding on launch), but I don’t have enough information on it for our purposes here. Using the Apollo CSM (or Zond, for that matter) for estimating the density of the Cylinder is a fairly poor assumption given the huge size difference between it and the Martian vehicle, but it’s all we’ve got and I’ll use it in place of wild-ass guessing.

I pulled the Apollo size and weight data from a press kit for the Apollo-Soyuz Test Project flight, which flew back in 1975.

After all the math (which I'll skip here), I got a total density for the Apollo CSM of 42.35 lbs. per cubic foot, including structure, fuel, consumables, astronauts, etc.

Assuming that the Cylinder is of the same density, this gives an overall weight for the Cylinder (on Earth) of:

W_{cylinder-Earth} = 72,700,000 pounds. (!)

(In case you’re checking me, I’m rounding this down to the nearest 100,000 pounds, giving the Martians the benefit of the doubt on more advanced, lighter structures than Apollo. Besides, any more accuracy than that is pointless given the root assumptions I'm making about density.)

On Mars, the weight is:

W_{cylinder-Mars} = 24,200,000 pounds.

That’s going to be one BIG gun, folks!

More later, with more calcs and less chat, I promise! ;-)

[Lensman]

I'm glad to see your return, Topaz! I look forward to more posts on the subject. Too tired to do more than skim your post at the moment, tho.

[Xav]

Topaz....First of all, glad you are back and gaining in health.

Second...my estimates were just throwing around figures for a solid walled cylinder made of titanium. Well, on reflection, that is just too crude. So I did calcs for a cylinder with two 'hulls' (inner and outer) seperated by a sort of support structure and came up with a density of around 10 lb/cuft...I neglected the end caps.

This density of the Apollo CSM....pity you didnt give references because, after browsing through as many sites as I could, I have turned up stuff which is very different to the figure of 42 lb/cuft. There are anomalies, to say the least.
On all the sites I found a figure of 218 cuft volume, which is absurd. To give a comparison, this would be equal to a crate 6 x 6 x 6, where as the CSM was a cylinder plus a cone 38 long and 13 dia. Using this and estimating the length of the cylindrical part as 28 feet, the volume comes out to be 4,070 cuft.

Now the weights. I hope these are more reliable than the quoted volume.
The CSM plus LM is about 99,000 lbs, this gives a density of 24 lb/cuft

Neglecting the LM....CSM weighs in at 67,000lb and this gives a density of 17 lb/cuft

(I have rounded everything sensibly here)

If the quoted volume of 218 cuft is taken, you come up with a ridiculous value of over 300 lb/cuft

I will be very interested as to your comments on this.

[Lensman]

Topaz: Hey, what gives with the old English units? I thought you and Lancer wanted to use metric 'cuz those units are easier to work with!

24,200,000 pounds = 10,976.94 metric tons. That's very nearly 4 times the weight of the loaded Apollo/Saturn V rocket. Ummm... yeah, as I said in an earlier post, that cylinder weighs JUST A BIT!!

Xav: I'd guess 218 cubic ft refers to the cockpit area, the open space, inside the command module. As you say, it's much too small for the combined volumes of the command & service modules.

[Topaz]

Xav - Quite right, I should've given my references! Bad Topaz, no cookie for me! ;D

I got the dimensions (in millimeters) from page 80 of the following PDF link:

www-lib.ksc.nasa.gov/lib/archives/apollo/pk/soyuz.PDF

I got the weight from:

www.answers.com/topic/project-apollo

One thing to keep in mind when calculating the density of this thing is that it's important to find the length of the CSM without the SPS engine bell. That was probably the toughest part of my search; finding a diagram that gave dimensions for each part of the spacecraft. Finding overall dimensions was easy, but if you use the total length of the vehicle the answer is skewed by all that empty space in and around the engine bell. I don't doubt your 17lb/cu. ft. density in that case. However, I wanted to use the density of the 'spacecraft proper' - without the engine bell - since that most closely approximates the Martian cylinder.

I'm also assuming (and a broad assumption it is!) that the Martian Cylinder will be similarly packed full of stuff like the Apollo vehicle, with both spacecraft-related things and the Fighting/Handling/Flying Machines, plus the crew space and consumables for the Martians themselves. I'm also assuming that the Cylinder will have some kind of propulsion system of its own, for mid-course corrections and such as have been discussed earlier in the "Uncontrolled Landing" thread.

The 218 cu. ft. volume is, indeed, the 'usable' volume inside the Command Module only.

I basically took the diameter and length of the cylindrical part of the Service Module (minus SPS and RCS thruster assemblies) and added a cone frustum on the front with the dimensions of the Command Module. From this, I got a total volume of 1,578 cu. ft., which I used to divide the 66,871 lb. weight from my source, to get the final 42.4 lb/cu. ft. density.

Lensman - Yep, I'm using 'Imperial' units, if for no better reason than I have a 'feel' for them (American, you know) and so can (hopefully) spot when I've made a gross error and have gotten an absurd answer!

And yes, the cylinder is freakin' HUGE!

Thank you both for the well-wishes, as well. It's good to be back.

I'll be back tomorrow with some more stuff - My math skills are occupied with doing my long-neglected taxes (due April 15th, here in the States).

[Xav]

OK, I will agree to all of your assumptions and the way you have put it all together but I still think that your volume is too low.
Unfortunately I cannot access the site to get the dimensions, so I am going to make the assumption that the rocket motor bell is about 8 feet long, so I will get a cylinder length of 20 feet and CM height of 8 feet and both with a dia of 13 feet.
This gives a volume of a little over 3000 cuft, hence a density of 22 lb/cuft.
There is nothing wrong with Imperial units....in fact I think they are very 'natural' units, but that is another story. I wonder if the Martians used base 16?

[Topaz]

Here's the Apollo CSM dimensions from the diagram:

Service Module Length (minus SPS): 4471mm = 14.67ft.
Service Module Diameter (minus RCS clusters): 3192mm = 10.47ft.

Command Module Length: 2446mm = 8.02ft.
Command Module Base Diameter: 3192mm = 10.47ft.
Command Module Nose Diameter: 3ft. (estimated)

From that, I get a volume for each of:

Volume_{Service Module} = 1263.5 cu. ft.
Volume_{Command Module} = 315.33 cu. ft.

The latter meshes nicely with the stated 218 cu. ft. 'usable' volume for the CM, leaving about 100 cu. ft. for control panels, batteries, etc.

Adding them up gives the 1578.83 cu. ft. I got for a total.

[Xav]

OK, Topaz, that clears that up and I have confirmed your figure from the dimensions given....Looking forward to the next part.