Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: holment on 17/12/2019 10:49:57
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When a rocket takes off it presumably gets very hot. Furthermore, we would imagine that it would cool down quite rapidly once it reached space, seeing as space is quite cold.
However, in a vacuum there are no molecules to transfer the heat.
Consequently, how fast will the rocket cool down, if at all?
Best
Tor
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It will cool down due to radiation. It is possible to estimate the time required for an object to cool due to radiation in a vacuum if you make some simplifying assumptions: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/cootime.html Using that calculator, a one meter, solid sphere of polished tungsten would require about 273 days to cool down from 1,000 Kelvins to room temperature (298 Kelvins). If the sphere is polished titanium, it requires 52 days. Silica requires just under 6 days. A sphere ten times wider takes ten times as long to cool down.
Take note that a rocket has a more complex shape than a sphere and is hollow (to an extent). The surface area to volume ratio would be much higher. As such I would expect it to cool down more quickly than a sphere. I may try to do some more precise calculations using a more realistic rocket shape in the future. There appears to be a linear relationship between cooling time and surface area. If you have two objects of the same composition and equal mass, and one has twice the surface area of the other, the one with double the surface area should cool twice as fast.
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seeing as space is quite cold
If you have a compressed gas expanding into a vacuum, it gets quite cold.
However, a solid object in Earth orbit is subject to different, competing, effects:
- The side directly facing the Sun (surface temperature around 5000C) is heated by about 1 kW per square meter, and gets quite hot.
- The side facing away from the Sun (and away from the Earth) is only exposed to the Cosmic Microwave Background Radiation, at a temperature around -270C, so it can get very cold
- The Moon rotates every 29 days, and has a temperature range of +130C in daytime to -170C (nighttime).
- If the Moon rotated more slowly, the temperature range would be even more extreme.
- Mercury rotates every 115 days, and has a temperature range of 430C to -170C
This is why most satellites are set to rotate, so that one side doesn't get too hot (and potentially weaken or overheat electronics) and the other side doesn't get too cold (and potentially become brittle, or freeze lubricants or batteries).
- Surfaces that must point in one direction for long periods of time (eg the Earth-facing antennas of geostationary satellites) are often covered in a thin layer of gold foil, which reflects away most of the heat on the hot side (high reflectivity), and does not emit too much heat into space on the cold side (low emissivity). Layers of insulation prevent the temperature variations of the gold penetrating the structure of the satellite.
In general, the farther you are away from the nearest star, the colder the average temperature.
- At Earth's orbit, the average temperature is about -15C
See: https://www.space.com/18175-moon-temperature.html
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I'll now consider a more rocket-like shape. The volume of a thin-walled cylinder can be calculated here: https://www.calculatorsoup.com/calculators/geometry-solids/tube.php
I'll assume a height of 16 meters and a diameter of 3 meters (similar to the second stage of the Titan II GLV). Wall thickness is tricky. Rockets are not uniform in thickness and indeed some areas can be very thin. I'll try a range of values: 1 centimeter, 5 centimeters and 10 centimeters: For the 1 centimeter-thick hull, the total volume is 1.5 cubic meters, for 5 centimeters it is 7.41 cubic meters, and 10 centimeters is 14.58 cubic meters.
This does not take into consideration "end cap" volume, however. The end caps can be modeled as flat, broad cylinders: https://www.mathopenref.com/cylindervolume.html For the 1 centimeter-thick hull, the total end cap volume is 0.14 cubic meters (for a total volume of 1.64 cubic meters). For 5 centimeters, it is 0.7 cubic meters (total is 8.11 cubic meters). 10 centimeters is 1.41 cubic meters (16 cubic meters). The corresponding external surface area for our cylinder is 165 square meters: https://www.calculatorsoup.com/calculators/geometry-solids/cylinder.php
A sphere with a total volume equal to 1.64 cubic meters has a radius of 0.73 meters. For 8.11 cubic meters, the radius is 1.25 meters. For 16 cubic meters, it's 1.56 meters. The equivalent surface area for each sphere is 6.7, 19.63 and 30.58 square meters respectively. The ratio between the surface area of each sphere and the cylinder is 0.04, 0.12 and 0.19 respectively. So the expected cooling times should be about 0.04, 0.12 and 0.19 times as long as for each equivalent volume sphere.
To help with your calculations, you can use this emissivity table: https://www.optotherm.com/emiss-table.htm
- A polished aluminum sphere (0.73 meter radius) at 500 Kelvins would cool down to room temperature in about 4.4 days (or about 4.2 hours for the equivalent rocket).
- A polished aluminum sphere (1.25 meter radius) at 500 Kelvins would cool down to room temperature in about 15 days (or about 1.8 days for the equivalent rocket).
- A polished aluminum sphere (1.56 meter radius) at 500 Kelvins would cool down to room temperature in about 18.8 days (or about 3.6 days for the equivalent rockets).
Some notes of caution: a real rocket will be made of multiple kinds of materials and have an uneven temperature across its surface (the nose cone will be much hotter than the sides). The hull will also be hotter on the outside than the inside. That makes a reliable calculation much more difficult to do.
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Does it really get that hot during launch? Concorde reached about 390 K when travelling for 3 hours at Mach 2 and 60,000 ft. A rocket will spend much less time in the lower atmosphere, with most of the acceleration taking place in vacuo. The problem then is direct heating from the sun on one side, rather than residual frictional heat.
The re-entry scenario is quite different. The capsule arrives at high speed and relies on atmospheric friction to slow it down, so the re-entry path is much longer and more energetic than the launch path through the atmosphere.
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Does it really get that hot during launch?
I was just making guesses, honestly.
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When a rocket takes off it presumably gets very hot. Furthermore, we would imagine that it would cool down quite rapidly once it reached space, seeing as space is quite cold.
However, in a vacuum there are no molecules to transfer the heat.
Consequently, how fast will the rocket cool down, if at all?
Best
Tor
Why would a rocket get hot when leaving the atmosphere? It only gets hot while returning as far as I know.
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Why would a rocket get hot when leaving the atmosphere?
Rockets get hot because of air "friction" as they get rammed through the atmosphere at high speed.
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When a rocket takes off it presumably gets very hot.
I guess you meant rocket engine, which gets hot due to combustion of the fuel.
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When a rocket takes off it presumably gets very hot.
I guess you meant rocket engine, which gets hot due to combustion of the fuel.
That is a strange guess to make just after I explained why rockets get hot.
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When a rocket takes off it presumably gets very hot.
I guess you meant rocket engine, which gets hot due to combustion of the fuel.
That is a strange guess to make just after I explained why rockets get hot.
Your explanation is indeed strange.
Why would a rocket get hot when leaving the atmosphere?
Rockets get hot because of air "friction" as they get rammed through the atmosphere at high speed.
https://www.spaceanswers.com/space-exploration/why-do-spacecraft-need-heat-shields-to-enter-earth-but-not-to-leave-it/
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Strange, but true.
So what?
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OP asked about a rocket when it takes off. Its speed isn't high enough to make it very hot due to air friction.
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OP asked about a rocket when it takes off. Its speed isn't high enough to make it very hot due to air friction.
You are right in that it isn't strictly friction.
That's why I put the word in quote marks.
Rockets get hot because of air "friction"
What actually causes most of the temperature rise is the sudden compression of the air just ahead of the rocket as it is forced out of the way.
The indicated temperature rises given here
https://sugarshotsolidworks.wordpress.com/2013/12/22/numeric-analysis-of-nose-cone-heating-first-steps/
are around 1000C
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The Primary cause of electronic failure is due to thermal cycling. The different materials expand at different rates and cause fractures between the silicon and solder joints to the substrates etc. In space Satellites are coated with heat reflectors but such things like solar panels are not. These must be experiencing some serious thermal cycling issues.
Satellite failures in space have been attributed to various things. The following link explains the obvious and not so obvious reasons for satellite failure.
http://www.dept.aoe.vt.edu/~cdhall/courses/aoe4065/NASADesignSPs/rp1390.pdf
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The indicated temperature rises given herehttps://sugarshotsolidworks.wordpress.com/2013/12/22/numeric-analysis-of-nose-cone-heating-first-steps/ are around 1000C
These figures refer to a small missile travelling continuously around Mach 5 in the lower atmosphere. The Saturn launchers reached Mach 12 after about 3 minutes but by this time were at 220,000 ft altitude. The atmosphere is considered "negligible" above about 100,000 ft, so rather different dynamic conditions applied, and the thermal mass of the nosecone was considerably greater than that of a guided missile.
Sorry I haven't found a better equation yet, but 1000 deg seems a lot higher than expected for a near-vertical lift into space.
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I can find data for the (much slower) concorde.
https://www.quora.com/How-hot-did-the-Concorde-fuselage-get-from-air-friction-during-full-speed-flight
It gets to about 150C
A simplistic calculation of the upper bound would be to assume that all the power that is dissipated as "drag" goes into heating the vehicle.
There is a point during the ascent where they have to throttle back the engines because the drag force of the air acting on the nose approaches the point where it may cause damage (once they are essentially out of the atmosphere, they can stop worrying about that and reopen the throttle).
If you multiply that force by the velocity you will get a power dissipation and, I think, much of that power is dissipated as heat.
Trying to establish the thermal mass involved would be tricky.
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If you multiply that force by the velocity you will get a power dissipation and, I think, much of that power is dissipated as heat.
I would tweak this back-of-the envelope calculation:
- From the force, you need to subtract the force that goes into accelerating the rocket: F=m(a+g)
- where m is the mass of the rocket
- g is the force of gravity (the rocket has to hold it up against gravity, until it approaches orbital velocity)
- a is the acceleration of the rocket, as it tries to reach orbital velocity
I agree that the remainder of the power goes into air resistance and heating
- Against this, you must balance the cooling effect of new, cold air rushing past the spaceship...
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The force that goes into accelerating the rocket isn't being used to push air out of the way.
So the force that gets large enough that they worry about the nose-cone strength is the force that gets multiplied by the velocity.
It is, of course smaller than the force supplied by the engines.
The subtraction has already been done.
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Huge difference between Concorde flying at 40 - 60,000 ft for several hours and generating aerodynamic lift (hence also drag) as it did so, and a rocket spending less than 4 minutes in the atmosphere with no aerodynamic lift component and hence minimal drag.
Thermal mass and diffusivity are crucial to determine surface temperature. You can regard the heat input to the rocket as being an adiabatic pulse lasting about 2 minutes as it accelerates from Mach 1 to Mach12, so the eventual surface temperature depends on the rate at which the sonic compression heating power is dissipated from the leading edges to the whole mass of the vehicle. The nose cone is in any case dumped in the cruise phase so as long as the surface doesn't melt and run over the separation joints, it doesn't really matter if it gets a bit hot. This is quite different from a low-level missile or supersonic aircraft, where the bits at the front are important throughout the mission!
I think the primary reason for "throttling back" is to maintain a reasonable g force. If you are burning at n tons/sec initially to get off the ground (g=1), the rocket weighs n tons less every second so g will increase if you hold a constant burn rate. 3 - 5 g is manageable but higher accelerations severely impair crew performance, hydraulic reliability and ultimately structural integrity of minimal structures like a LEM. The difference between early "slam-bang" manned rockets and Saturn was described by astronauts as "an old man's ride" - I gather the Soyuz is equally civilised.
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I think the primary reason for "throttling back" is to maintain a reasonable g force.
You may think that, but
(1) it's not what the guys at the space centre said and
(2) it doesn't make much sense.
At a given throttle setting and thus a given power the acceleration will naturally reduce as the velocity rises. The rate of change of mass is pretty impressive, but, at that point, the rocket is essentially "still full". It's about 50 seconds into the flight. The shuttle's about the height of Everest at that point- there's plenty of air in the way.
There's no physiological need to reduce the acceleration at that point; physics does that for you.
https://en.wikipedia.org/wiki/Max_q
There is a later point where they throttle back the engines to stop the acceleration squashing the astronauts.
That's about 7.7 minutes into the flight. it's a long way up- past most of the air.