Rocket/missile range change with weight?

[Arugela]

I wasn't able to figure this out.

I'm looking at an example of the Midgetman program prototype stuff. Assuming you could stick a moab on the top what range would it have. Assuming you didn't change the fuel.

https://en.wikipedia.org/wiki/MGM-134_Midgetman

https://en.wikipedia.org/wiki/W87#Variants

The rocket is listed on wiki as 30,000lbs with what appears to be up to 4 x 600 lbs(2400lbs) W87 warheads.

Midgetman: 7000 miles; 30,000 - 2400 = 27,600lbs

Moab: 21,600lbs

27,600+21,600= 49,200lbs.

What would the range be if this was possible. I think the moab is exactly 9 times the weight of the 4 other warheads combined and around 1.64 times the weight of the basic midgetman(with warheads/30,000lbs).

Is this a linear relationship or does it follow 2 or 3 dimensions? Or something else? (I used a calculator and I'm assuming it's somehow 2 dimensional)

Edit: Would it get around 35 miles max range?

 

Edited Friday at 04:30 AM by Arugela

[Gargamel]

Even without knowing the engine stats, a simple application of the rocket equation should given you an energy ratio in terms of those engine stats, since it’s using the same engine for both.     And while dV is not linearly applicable to range, you could then at least estimate a max range.   And with a little more research, you could possibly figure out those engine stats and give you exact dV numbers, which would give you your max apogee for the optimum MIRV reentry profile (ICBM’s have different flight paths than standard more intuitive rockets), and therefore your max usable range.  
 

But to be fair, my understanding of the rocket equation is just enough to sound like I know what I’m talking about when it’s actually just flatulence.      Somebody should be around soon enough to correct me.   
 

 

But honestly, my gut is telling me the max range is zero.    I doubt that engine has enough thrust to lift that much payload.  

[Terwin]

Maximum dV is usually achieved with a TWR close to 1.

There may be a desire to 'get them out' quickly, and thus have a higher TWR at launch.

a TWR of 1.1 is fairly high, Super heavy with Starship has a TWR of 1.4, which is rather high  (according to this 6 year old reddit thread: https://www.reddit.com/r/SpaceXLounge/comments/ae79vi/any_idea_about_the_thrustweight_ratio_of_super/ )

Anything over 1.5 is often considered wasteful for a rocket.

Your missile would need a TWR of 1.64 to get off the ground.

Missiles will often have a higher TWR for the sake of speed(and not getting shot down)

Wiki (https://en.wikipedia.org/wiki/Intercontinental_ballistic_missile ) says that ICBMs burn for 3-5 minutes to a velocity of 4km/s with solid fuel burning out faster.

If we take 4000m/s  over 180 seconds we get an average thrust of 22.2 m/s/s

The best possible scenario for your heavy rocket would be a thrust of ~32m/s/s  which would result in a total thrust of 19.5m/s/s or a twr of just under 2 for your version  compared to a little over 3 for the original.

But that would be a very poorly designed rocket because it would almost always be throttled lower than it could be.  Usually you get much more thrust towards the end of your burn than towards the beginning, so you would probably spend a significant percentage of your fuel before lifting off, just because the engine is too weak to lift the much higher mass.

 

[kerbiloid]

First stage:

Space rockets: TWR ~1.2

ICBM: mid-XX ~1.5, late-XX ~2

ABM: as much as possible

Next stage: 0.8..1.2.

 

But what's a connection between the Midgetman (rocket) and MOAB (bomb)?

Edited Saturday at 04:52 AM by kerbiloid

[magnemoe]

4 hours ago, kerbiloid said:

First stage:

Space rockets: TWR ~1.2

ICBM: mid-XX ~1.5, late-XX ~2

ABM: as much as possible
Next stage: 0.8..1.2.

But what's a connection between the Midgetman (rocket) and MOAB (bomb)?

Seems right, for an ICBM and other missiles you want an higher TWR for faster travel time, harder so intercept during launch and better accuracy as an slow takeoff would be more affected by wind. 

Starship has an high TWR as they want it to get up to speed and attitude to drop second stage fast so the boost back burn will be shorter. 
If you can land downrange the TWR is less important. On an single use rocket without SRB like the Saturn 5 an low TWR makes sense as making the tank larger and adding fuel is the cheaper part of an rocket.

[Arugela]

13 hours ago, kerbiloid said:

First stage:

Space rockets: TWR ~1.2

ICBM: mid-XX ~1.5, late-XX ~2

ABM: as much as possible

Next stage: 0.8..1.2.

 

But what's a connection between the Midgetman (rocket) and MOAB (bomb)?

I was just wondering if it could be put on it since it doesn't have a method of launch besides C130's and it would be a cool combo. And midgetman is the only vehicle launcher I could find in the US arsenal to go with it. I didn't think about the total thrust of the rocket as an issue. Could a custom rocket of that size get the needed/ideal thrust?

Edited Saturday at 06:31 PM by Arugela

[magnemoe]

21 hours ago, Arugela said:

I was just wondering if it could be put on it since it doesn't have a method of launch besides C130's and it would be a cool combo. And midgetman is the only vehicle launcher I could find in the US arsenal to go with it. I didn't think about the total thrust of the rocket as an issue. Could a custom rocket of that size get the needed/ideal thrust?

Wonder if reason its not used from bombers is that it has so low density? Even an B-52 would not be able to carry an so large bomb but an smaller could work. 
Its also an pretty specialist weapon, think its most useful clearing minefields or destroying strong field fortifications but for the later I guess an B-52 with standard bombs would also work well. 

Not sure how well it would work on an ICBM for one it would be an comical large payload KSP style also you don't want to drop it too fast as it need to disperse the fuel into the air and then ignite. 

[Arugela]

I wonder if you could then just slap larger wings on it and launch it from a c130...

How much distance does a glider get like that? I'm not sure on the math for gliders. I'm assuming it would need ridiculously large wings.

I believe it's:

length: 31ft

weight: 21600lbs(10.8tons)

Diameter 3ft6inch? approximately.

Current wings: 5 ft (10ft total or when popped out? I assume total.*C130 has a 10ft opening.) Unsure of the length. I'm assuming 10-15ft max.

Current minimum safe launch in a c130 is 6000ft.

Max altitude with payloads of C130 is max 33,000ft with older models down to 26,000ft at 42-45k lbs.

Not sure on the wing loading currently. Plus it has the same fins as the bottom stage of the SpaceX rockets.

I would assume you would need some sort of massive pop out wings as it's currently at the maximum for release in a C130. I'm assuming structural needs would make those some thick wings and limit the size drastically if it's not already at the extreme limits. Does anyone know what the current glide distance is for the Moab? If it has one effectively. I'm assuming not. (it might need 4 diagonal pop out wings)

It's also designed with a fairly thin aluminum skin to maximize the filler. I wonder if it has limits for air drops from that also.

Edited 2 hours ago by Arugela