Environmental effects of a spaceship landing

What if in a massive display of power, in the future a human military would build a massive spaceship with huge rocket engines and decided to land the craft vertically onto a desert in a magnificent show of force

here is a picture I found to get a sense of scale of the engines I am talking about

-Ship is approx 7 million tons (this is subject to change as answers come in and people adjust the weight to something more scientifically more accurate)

-Height: 5280 feet tall

-Diameter: 2000 ft

• For the purposes of the hypothetical situation just assume here are 7 engines of the size in the picture above

-Fuel is not an issue, they are basically showing off their might and the fact they can waste huge amounts of it without ever running out.

-Once landed the ship can stand on its own and there is no possibility of it falling over

Edit:

-assume it is landing in the Sahara desert on earth

• the landing soft and it touches down lightly

question:

1.What are the immediate effects on the surrounding area if such a craft landed?

2.What would happen to the desert below? would there be any significant changes to the environment due to such large rockets heating everything up/ large object touching down on the ground?

3.What would be the max distance you would have to be from the landing to survive?

• Wouldn't this largely be based on HOW it landed? If it just hurled itself at the ground, The massive heat added to the atmosphere from reentry would have major affects on the climate. And if it lands with burners, you would now have a glass dessert... and I don't know what a mini-moon on a giant pane of glass on the ground would do X3 – Tezra Sep 30 '16 at 17:18
• The ship has a volume of about 4 million cubic metres. Those engines appear to be chemical rockets. Is that 7 million tons empty weight, or with fuel on board? – John Dallman Sep 30 '16 at 17:37
• I was hoping that the fuel wouldn't matter because for the purpose of the question its assumed that they have enough to land it and take off again – totally not rick sanchez Sep 30 '16 at 18:06
• If we are talking modern tech, it should be worth mentioning that it takes more fuel than the weight of that fuel to get that weight of fuel to space (link) And that reaching space is only possible because as you burn fuel, the rocket gets lighter. So there would be a massive weight difference pre and post take off of this ship. – Tezra Sep 30 '16 at 19:10
• *You need more fuel to get your fuel into space My previous wording was a bit off. – Tezra Sep 30 '16 at 19:20

Assumption 1: Landing a spaceship softly takes the same rocket burn as it it does to launch it.

Assumption 2: You are envisioning this spacecraft taking off and landing like Saturn V. I'm only going to calculate the taking off/landing part.

Assumption 3: The spaceship has the same density as a Nimitz carrier. Estimating this ship at 5 times the length and 10 times the diameter of a carrier, the mass will be roughly $5\cdot10\cdot10 = 500$ times greater, or 50 million tons (5e10 kg).

Assumption 4: You can scale a Saturn V up linearly by strapping a whole bunch together (which is what your picture looks like). I'll only compare to the first stage, since you seem to be interested in the blast damage to the planet.

Assumption 5: Ignore fuel requirements. Logistics are for professionals, we're perform calculations on things that go boom.

If the Saturn V produced 35MN to lift off 3e6 kg, then you need 5.8e11N to lift off 5e10 kg, or half a teraNewton, if you like to use units that not many people talk about. Energy is force times distance, so if we say (another assumption) that the rocket affects the earth until it is a mile in the air, multily 5.8e11 N by 1500m to get 8.8e14 J of energy release.

Lets stack few more turtles to stack on this pillar of assumptions. I'm going to use a conservation of energy estimate to see what all this energy release would do.

This site says that 30% of that energy is released as waste heat. Lets say all that heat is transferred to the sand: the sand just got 2.63e14 J hotter.

The accepted answer here says that it is 1.5 MJ to turn a kilo of sand into glass. That means we can melt 1.8e9 kg of sand. At a density of 1400 kg/m$^3$, that means we melted 125000m$^3$ of sand. Make that a perfect half-sphere and you have about a 40 m^3 sphere of sand. So that would be a significant environmental change.

Lets take those other 70% of energy and convert it into wind energy to simulate a blast wave. That is 6.1e14 J of energy. If we give all the air in a 40 m$^3$ radius, to a height of, say 10m (to simulate a shockwave along the ground) that much kinetic energy, how fast would it be rushing outwards? Well that is a volume of 5e4 m$^2$ of air, with mass of 6e4 kg, so it would pick up a velocity of 141047 m/s. Holy smokes! So the blast wave would probably be more damaging to your safety than the heat.

Lets solve for the distance you need to be to get the air speed down to 50 m/s, which is strong, but unlikely to kill you. I calculate 112 km. Seems high. Lets raise the height of the shock wave to 100m: now we're at 36 km.

Ok so that post will not hold up to any scrutiny, but I can guesstimate your answers as:

1.What are the immediate effects on the surrounding area if such a craft landed?

Anything withing a kilometer is probably killed by heat. Powerful shock wave up to 10km, hurricane force winds beyond that.

2.What would happen to the desert below? would there be any significant changes to the environment due to such large rockets heating everything up/ large object touching down on the ground?

Yes, there would be a lot of glass.

3.What would be the max distance you would have to be from the landing to survive?

The max distance would be the opposite side of the planet. The minimum distance would be somewhere from 10-50km.

It really depends on engines they use(ISP), and maximum deceleration speed they are comfortable with, speed they approach.

Maximum punishment with photon engines, decelerating in milliseconds, from speed close to speed of light - and there actually almost no limit how much energy they can deliver.

With something less exciting like 4000m/s exhaust velocities (ISP 407 sec) - they are a bit limited in energy they can deliver. Higher ISP is, more energy they can deliver, with the same approach speed.

But let say they have ISP=407sec, approach speed also not exciting let say 4000m/s, deceleration rate also let say 2g - time to decelerate 200 sec. Mass 7'000'000 tonnes.

Deceleration path will be 400km, pretty long distance, where energy will be distributed. Even for vertical landing, when energy kinda will be directed to one spot on earth surface, but because of distance it will be eventually distributed over large volume in earth atmosphere.

Power produced by engines will be 280'000GW (7000000000 * 20 / 4000 * 4000^2 / 2)
or it is equivalent to 66kT nuclear blast each second.

if that all energy will be applied to one spot on surface (which it not, not all, not on one spot, but to determine maximum in that case we assume it is) - it will be 13.2MT blast
According to nukemap it is:

• Air blast radius (5 psi): 16.4 km (850 km²)
At 5 psi overpressure, most residential buildings collapse, injuries are universal, fatalities are widespread. Optimal height of burst to maximize this effect is 7.38 km.

This is kinda maximum energy deployed, and maximum effect of such actions. Also it give to us first approximation of optimal height.

Second approximation is low border, ship blasts 66kt each second, let say it is only one blast 66kt

• Air blast radius (5 psi): 2.81 km (24.8 km²)
At 5 psi overpressure, most residential buildings collapse, injuries are universal, fatalities are widespread. Optimal height of burst to maximize this effect is 1.26 km.

• Fireball radius: 330 m (0.33 km²)
Maximum size of the nuclear fireball; relevance to lived effects depends on height of detonation. If it touches the ground, the amount of radioactive fallout is significantly increased. Minimum burst height for negligible fallout: 290 m.

It give to us some sort of minimal distance for zone we consider safe for 1 sec working engine, at height 1.26km, with lesser height safe distance will be less then 2.8km.
Fireball radius it is where we expect sand to melt etc.

Now we are back to engines, how long they can work. They can have some kind of thermonuclear power, and use atmosphere as reactive mass and hover over desert indefinite time converting it to one big glass by traveling back and forth and creating hurricanes - there are infinite application for infinite energy.

If it is just 2g descent - my guess we can expect some effects from 5km height, 22 seconds of descent for that ship, 22 consecutive blast with 66kt yield, 1452kt total, max estimation Air blast radius (5 psi): 7.88 km, efficient height 3.54km.

Conclusion

Distance 10 km I would call relatively save distance, experience will be may be not pleasant, but not fatal.

Overall, no planetary scale catastrophe or something like that, but sure it will be noticeable for long distances, hundreds of km.