Is a Space Shuttle launch as powerful as an “average” nuclear explosion? [closed]

First let's define what an "average" nuclear explosion is, because that's quite a controversial term - "average". Considering that the peak of nuclear tests was at the 1960s, and that the bulk of nuclear or thermonuclear devices developed in that period were fission bombs, and disregarding radical developments like the Tsar Bomba or the B41 nuclear bomb, I'd say it's safe to proclaim an explosion yielding ~800t of TNT is average on these terms.

To back up my numbers I cite the statistics for 60s-era nuclear tests, like Operation Nougat, Operation Dominic, Operation Whetstone, Operation Latchkey and Operation Flintlock. The numbers are readily available on Wikipedia.

Now to the Space Shuttle.

The solid rocket boosters (SRBs) of a Space Shuttle exert 14MN ($14\times10^6$ newtons) of thrust each shortly after liftoff, and provide 80% of thrust for the whole stack until they are jettisoned at $46\:\mathrm {km}$ above sea level. Their thrust level is constant until the fuel is burnt and depleted.

The SSMEs (Space Shuttle Main Engines each produce ~2MN of thrust at 100% throttle up until the Shuttle reaches orbit at $320\:\mathrm{km}$ altitude.

Considering that work can be measured in Newtons per meters, ie., J = Nm, therefore:

SRBs:

1. $14\times10^6\:\mathrm{N} \times 46\,000\:\mathrm m = 644\times 10^9\:\mathrm J$

2. $\times2$ SRBs $= 1\,288\times 10^9\:\mathrm J$

SSMEs:

1. $2\times 10^6\:\mathrm N \times 320\,000\:\mathrm m = 640\times 10^9\:\mathrm J$

2. $\times 3$ SSMEs $= 1\,920\times 10^9:\mathrm J Total: SSMEs + SRBs$= 3\,208\times10^9\:\mathrm J$or$3.2\times 10^{12}\:\mathrm J$or$3.2\:\mathrm {TJ}$. 1kt of TNT equals$4.184\:\mathrm {TJ}$, therefore, one Space Shuttle launch is equal to around 760 tons of TNT across the whole$320\: \mathrm{km}$stretch. Did I get the work/energy/force relationships right? • "yielding ~800t of TNT " Er...you are off by some orders of magnitude. Did you mean ktons? Even the Trinity bomb was about 20 ktons TNT equivalent. Which, of course throws the whole speculation off. – dmckee Jan 28 '14 at 14:58 • Just briefly glancing at the wikipedia page you cited, all of the detonations listed save one were well above 800t of TNT. I'd say the average seems closer to 5kt. Which would tend to put your energies on different orders of magnitude – Jim Jan 28 '14 at 14:58 • This info-graphic says a single launch uses about as much energy as a family does in a year (about 10,000 kWh ~$36\times10^9\$ J), significantly smaller than your TJ value. – Kyle Kanos Jan 28 '14 at 14:58
• Seriously guys, look into the operations I linked. There is a multitude of experiments yielding much less than a single kiloton. – pilau Jan 28 '14 at 15:16
• @pilau I would like to repeat that I did check your links and I found 12 explosives across three operations that were listed as having caused less than 1kt each. However, a multitude more seem to have caused between 1kt and 5Mt, which would drastically skew the average above 800t TNT – Jim Jan 28 '14 at 15:20

1 Answer

A hamburger's enthalpy of combustion equals TNT's enthalpy of detonation. Energy proposes, power disposes. Consider a 100 W bulb running for an hour vs. the same total energy handled within a microsecond, 100 W vs. 360 GW. A Space Scuttle detonation would have transpired over minutes (mixing plus propagation time) vs. nuclear microseconds.

Now, coupling efficency! Coals' enthalpies of combustion are 2.4-3.2×10^7 J/kg. Rule of thumb: 5 eV/O2 molecule consumed, thus 4×10^7 J/kg (-393.7 kJ/mol) for pure carbon oxidized to CO2. Body in low Earth orbit, v^2 = Rg, kinetic energy/kilogram = Rg/2. With R = 6×10^6 m (from the center of mass) and g = 10 m/s^2, 3×10^7 J/kg (gee = 8.40 m/sec^2 at 300 miles altitude). Burning a lump of anthracite should orbit it! (OK, less mgh.) A rocket uses 100× as much energy/kilogram. The Space Scuttle was astoundingly inefficient for boosting mass into orbit since most of its payload was its useless self.