Editing Rocket (section)

===Energy===

====Energy efficiency====
{{Main|propulsive efficiency}}
[[File:Atlantis taking off on STS-27.jpg|thumb|{{OV|104}} during launch phase]]

The energy density of a typical rocket propellant is often around one-third that of conventional hydrocarbon fuels; the bulk of the mass is (often relatively inexpensive) oxidizer. Nevertheless, at take-off the rocket has a great deal of energy in the fuel and oxidizer stored within the vehicle. It is of course desirable that as much of the energy of the propellant end up as [[kinetic energy|kinetic]] or [[potential energy]] of the body of the rocket as possible.

Energy from the fuel is lost in air drag and [[gravity drag]] and is used for the rocket to gain altitude and speed. However, much of the lost energy ends up in the exhaust.<ref name="RPE7"/>{{rp|37–38}}

In a chemical propulsion device, the engine efficiency is simply the ratio of the kinetic power of the exhaust gases and the power available from the chemical reaction:<ref name="RPE7"/>{{rp|37–38}}

{{block indent|<math>\eta_c= \frac {\frac {1} {2}\dot{m}v_e^2} {\eta_{combustion} P_{chem} }</math>}}

100% efficiency within the engine ([[Heat engine#Efficiency|engine efficiency]] <math>\eta_c = 100\%</math>) would mean that all the heat energy of the combustion products is converted into kinetic energy of the jet. This is not possible, but the near-adiabatic [[rocket engine nozzle|high expansion ratio nozzles]] that can be used with rockets come surprisingly close: when the nozzle expands the gas, the gas is cooled and accelerated, and an energy efficiency of up to 70% can be achieved. Most of the rest is heat energy in the exhaust that is not recovered.<ref name="RPE7"/>{{rp|37–38}} The high efficiency is a consequence of the fact that rocket combustion can be performed at very high temperatures and the gas is finally released at much lower temperatures, and so giving good [[Carnot efficiency]].

However, engine efficiency is not the whole story. In common with the other [[jet engine|jet-based engines]], but particularly in rockets due to their high and typically fixed exhaust speeds, rocket vehicles are extremely inefficient at low speeds irrespective of the engine efficiency. The problem is that at low speeds, the exhaust carries away a huge amount of [[kinetic energy]] rearward. This phenomenon is termed [[propulsive efficiency]] (<math>\eta_p</math>).<ref name="RPE7"/>{{rp|37–38}}

However, as speeds rise, the resultant exhaust speed goes down, and the overall vehicle energetic efficiency rises, reaching a peak of around 100% of the engine efficiency when the vehicle is travelling exactly at the same speed that the exhaust is emitted. In this case the exhaust would ideally stop dead in space behind the moving vehicle, taking away zero energy, and from conservation of energy, all the energy would end up in the vehicle. The efficiency then drops off again at even higher speeds as the exhaust ends up traveling forwards – trailing behind the vehicle.

[[File:Average propulsive efficiency of rockets.png|thumb|Plot of instantaneous propulsive efficiency (blue) and overall efficiency for a rocket accelerating from rest (red) as percentages of the engine efficiency]]From these principles it can be shown that the propulsive efficiency <math>\eta_p</math> for a rocket moving at speed <math>u</math> with an exhaust velocity <math>c</math> is:
{{block indent|<math>\eta_p= \frac {2 \frac {u} {c}} {1 + ( \frac {u} {c} )^2 }</math><ref name="RPE7"/>{{rp|37–38}}}}

And the overall (instantaneous) energy efficiency <math>\eta</math> is:
{{block indent|<math>\eta= \eta_p \eta_c</math>}}

For example, from the equation, with an <math>\eta_c</math> of 0.7, a rocket flying at Mach 0.85 (which most aircraft cruise at) with an exhaust velocity of Mach 10, would have a predicted overall energy efficiency of 5.9%, whereas a conventional, modern, air-breathing jet engine achieves closer to 35% efficiency. Thus a rocket would need about 6x more energy; and allowing for the specific energy of rocket propellant being around one third that of conventional air fuel, roughly 18x more mass of propellant would need to be carried for the same journey. This is why rockets are rarely if ever used for general aviation.

Since the energy ultimately comes from fuel, these considerations mean that rockets are mainly useful when a very high speed is required, such as [[ICBM]]s or [[orbital spaceflight|orbital launch]]. For example, [[NASA]]'s [[Space Shuttle]] fired its engines for around 8.5 minutes, consuming 1,000&nbsp;tonnes of solid propellant (containing 16% aluminium) and an additional 2,000,000&nbsp;litres of liquid propellant (106,261&nbsp;kg of [[liquid hydrogen]] fuel) to lift the 100,000&nbsp;kg vehicle (including the 25,000&nbsp;kg payload) to an altitude of 111&nbsp;km and an orbital [[velocity]] of 30,000&nbsp;km/h. At this altitude and velocity, the vehicle had a kinetic energy of about 3&nbsp;TJ and a potential energy of roughly 200&nbsp;GJ. Given the initial energy of 20&nbsp;TJ,{{#tag:ref|The energy density is 31MJ per kg for aluminum and 143&nbsp;MJ/kg for liquid hydrogen, this means that the vehicle consumed around 5&nbsp;TJ of solid propellant and 15&nbsp;TJ of hydrogen fuel.|group=nb}} the Space Shuttle was about 16% energy efficient at launching the orbiter.

Thus jet engines, with a better match between speed and jet exhaust speed (such as [[turbofans]]—in spite of their worse <math>\eta_c</math>)—dominate for subsonic and supersonic atmospheric use, while rockets work best at hypersonic speeds. On the other hand, rockets serve in many short-range ''relatively'' low speed military applications where their low-speed inefficiency is outweighed by their extremely high thrust and hence high accelerations.

====Oberth effect====
{{Main|Oberth effect}}
One subtle feature of rockets relates to energy. A rocket stage, while carrying a given load, is capable of giving a particular [[delta-v]]. This delta-v means that the speed increases (or decreases) by a particular amount, independent of the initial speed. However, because [[kinetic energy]] is a square law on speed, this means that the faster the rocket is travelling before the burn the more [[orbital energy]] it gains or loses.

This fact is used in interplanetary travel. It means that the amount of delta-v to reach other planets, over and above that to reach escape velocity can be much less if the delta-v is applied when the rocket is travelling at high speeds, close to the Earth or other planetary surface; whereas waiting until the rocket has slowed at altitude multiplies up the effort required to achieve the desired trajectory.