# Object’s speed and its heating temperature

1. Apr 27, 2010

### Eagle9

When some certain object (asteroid, aircraft, spaceship and etc.) moves at great velocities into Earth’s atmosphere it heats. The faster its moves and the denser is the atmosphere the heater this certain object becomes. This is simple is clear. Now, is it possible somehow to predict or calculate this heating temperature? For instance, the object moves at the speed of 975 meter/sec at the altitude of 80 km above the sea level, can we calculate its heating temperature? Are there some formulas in Physics or ready-made charts/diagrams for this purpose? I need this data for the altitude of 0-160 km above the see level…

2. Apr 27, 2010

### Staff: Mentor

No easly calculation: it is specific to the geometry (and other properties) of the object.

3. Apr 28, 2010

### Eagle9

Well, let’s assume that it is long tube with the diameter of 5 meters, now it could be calculated?

4. Apr 28, 2010

### kcdodd

You might be able to get a rough estimate by looking at the drag force. The drag is caused by several things, but friction is one, and that is what causes the heating. Force time velocity gives your heating power. So, you need to look up the drag coefficient for the object in question.

5. Apr 28, 2010

### Eagle9

So, if I understood correctly I need to find the drag coefficient? And where is it possible to find it? Are there some ready-made charts?

6. Apr 28, 2010

### log0

Look for: skin friction coefficient, supersonic drag, slender body

Here is an online calculator for a flat plate(link at bottom of the page):

The drag for given air density, velocity, surface area, friction coefficient is:

$$D = 0.5 \rho v^{2} S C_{f}$$

Just to get an idea:
The SR-71 has surface temperatures above 300 degrees celsius at 980m/s(MACH 3.2) and 24km height.

Edit:
You might try to find some surface temperature data from the X-15 program.

Last edited by a moderator: Apr 25, 2017
7. Apr 28, 2010

8. May 4, 2010

### Eagle9

Ok, thank you very much, I think this is what I wanted . However, I would like to specify some issues since I am not physicist and sometimes it is a bit difficult for me to understand some problems in this science.
First of all, here is the illustration what I actually wanted to know. Imagine a long and thin rod is rotating in the atmosphere with various angles of attack. I want the result for the situation when this rod has got almost vertical position-70°, 80° or 90°.
http://img576.imageshack.us/i/engd.gif/ [Broken]

Frankly saying I do not know properties of which gas (calorically perfect gas or calorically imperfect gas) should be calculated for the real Earth’s atmosphere. As I know perfect gas does not exist in the nature at all, therefore I need to measure property of imperfect gas, right? I read the information presented in the web-link given by you. If I understood everything correctly I need the Total Temperature calculated in the Java calculator, right? So, as an example, I put the following values: the object moves in the atmosphere at the altitude of 80 000 meters (by the way after the calculation this value for some reason was decreased to 76 200 meters) at the speed of 975 meters/sec. After computations I saw the following result: Total Temperature is equal to 646 Kelvin degrees (for imperfect gas). Is it right? So, this object would be heated to the temperature of 646 degrees?
http://img504.imageshack.us/img504/8301/calculatoru.jpg [Broken]

I have actually got one more question. For which altitudes this derived result (646 degrees K) is correct? For the whole section of the atmosphere from the seal level to the altitude of let’s say 150 km above the sea level? Or there are some limitations?

Last edited by a moderator: May 4, 2017
9. May 19, 2010

### Eagle9

Ok, thank you very much, I will take look at it

Last edited by a moderator: Apr 25, 2017