# Question of the Week

## At what speed does windchill give way to frictional heating?

Sat, 28th May 2011

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### Question

I recently started commuting by bicycle, but now that it's becoming winter, I've been wondering more about windchill. I understand much of it involves the moisture in the air, but how come commercial airplanes land from flights with cold icy surfaces, while some supersonic jets and reentering spacecraft land with a hot surface because of atmospheric friction?

At what point is the threshold?

Is there a room temperature flight velocity?

And how fast will I need to ride my bike for atmospheric friction to overcome windchill and keep me warmer?

We put this question to Kevin Knowles from Cranfield University and Holger Babinski from Cambridge University...

Kevin -   I'm Kevin Knowles.  I'm professor of aeromechanical systems for Cranfield University and I work at the Defence Academy of UK in Shrivenham, Oxfordshire.  In essence, the answer to the question is that aircraft wings are cold because they fly high in the atmosphere, the region known as the troposphere, and atmospheric temperatures fall with altitude in the lower atmosphere.  So an aircraft flying at about 10 kilometres which is typical above the ground, a day where it’s only 15 degrees Celsius at sea level, will be experiencing temperatures of about minus 50 Celsius outside.  If however, you move fast enough in excess of the speed of sound then there's a significant kinetic heating effect and that's what spacecrafts experience.  For example, if an aircraft were again flying at 10 kilometres altitude, but now at nearly at 7 " alt="An F/A-18 Hornet breaks the sound barrier in the skies over the Pacific Ocean." />times the speed of sound, then the temperature that it would feel due to kinetic heating, the highest temperature would be about 10 times the ambient temperature, but measured in degrees Kelvin.  Now 10 kilometres altitude, the temperature in Kelvin is 223, so Mach 7 spacecrafts would experience 10 times that, so its heat temperature would be 2,200 Kelvin or about 2,000 degrees centigrade.  At 10 kilometres, those two effects balance out if you're flying at about Mach 1.2, so at that speed, the kinetic heating is just enough to bring the peak skin temperature up to sea level temperature.

Diana -   So it’s not so much the wind-chill effect as the fact that planes fly around in the colder part of the atmosphere.  Travelling at Mach 2, Concorde used to experience surface temperatures over 100 degrees Celsius causing the fuse lodge to extend by as much as a foot, but what if you're a cyclist?

Holger -   Hello.  My name is Holger Babinski and I'm professor of aerodynamics in the engineering department of Cambridge University.  How much friction you need to compensate for the fact that the air is cold around you, depends very much on the temperature difference between your body temperature and the air temperature.  You asked how fast you would have to cycle, so I shall assume that you're cycling at sea level.  There, the surrounding temperature on a cold day might be something like 17 degrees.  And in order to generate enough friction to bring the air up to body temperature, you have to cycle at about 63% of the speed of sound.  With the speed of sound at sea level, that is pretty much 480 miles per hour.  So you have to be pretty fast to achieve that.

#### Make a comment

In this case, cooling comes by water evaporation and heating comes from friction of air moving over surfaces.
If you remove the cooling effect, you should feel warmth of air friction when bicycling.
This can be done your exposed skin with a petroleum jelly (vaseline for example) which would prevent sweat evaporating in the wind, then allowing the heating effect of the wind to be experienced.
However, don't blame me if the vaseline causes you to slide off the bicycle and suffer injury
diverjohn, Wed, 25th May 2011

Not only by evaporation DJ. Heat is also removed from the surface of the skin by conduction. Geezer, Wed, 25th May 2011

Not only by evaporation DJ. Heat is also removed from the surface of the skin by conduction.
how does "wind chill factor" play into this? CZARCAR, Wed, 25th May 2011

how does "wind chill factor" play into this?

Wind Chill Factor likely has components of both evaporation (humidity + wind speed) and conduction/convection.

The convection/conduction is that your body would essentially warm an envelope of air around it.  If that envelope is removed by wind, then you will feel colder.

I was going to say that you couldn't overcome wind chill, but the Space Shuttle and various spacecraft, and meteorites obviously experience heat due to wind friction.

Mach 1?

Perhaps I should rig up a thermometer and try the test on the freeway.  Do you think the highway patrol would buy the argument that one was just conducting a science experiment?  Not that I have a car capable of going over 100 MPH. CliffordK, Wed, 25th May 2011

For conductive heat loss, you likely have 2 (or more) equations.

Heating:
Likely something like 1 degree heating per every 100 mph (starting at 0 mph).
So, an equation of the form:
Temperature Object(Actual) = Temperature Object(Intitial) * (Wind Speed / 100)

Cooling (conductive/convective heat loss, ignoring evaporation).
Based on difference between object temperature and wind temperature.
It would reach an asymptote at the wind temperature (again ignoring evaporative heat loss).

Temperature Object(Actual) = Air Temperature + ((Temperature Object(Intitial) - Air Temperature) / (Wind Speed + 1))

Now that you have 2 equations, you would solve for the Temperature Object(Actual) = Temperature Object(Initial) for non zero wind speeds.

I just made up the constants, but the equations would be similar.

What pops out of this...
If the Air Temperature > Object Temperature, then you should see both conductive/convective heating AND Friction heating for all wind speeds > 0 (again ignoring evaporation).

If the Air Temperature < Object Temperature, the you could likely simplify the second equation by setting the temperature difference to being the difference between the object temperature and the air temperature, then solving the first equation for that difference.

Perhaps I'm calculating temperature when I should be calculating heat flux.  It probably would depend on surface area and turbulence.  And, for the convective/conductive heat loss, it would also depend on the ability of the object to compensate.

But, the idea would be the same.

For friction, the heat flux would increase linearly, or perhaps logarithmically with wind speed, and always be positive.

For convection/conduction, the heat flux would be similar.  Still bound by the difference of object and air temperatures, but also dependent on the ability of the skin of the material to conduct temperature.

Altitude and density of the air would also factor in somewhere. CliffordK, Thu, 26th May 2011

The power required to move a vehicle thru the air varies as the cube of the speed so presumably the heating effect varies in the same manner at least at subsonic speeds. syhprum, Mon, 13th Jun 2011

The point at which frictional heating overcomes convection cooling on your skin is a velocity that will sand blast you away. willyp00, Fri, 4th Nov 2011

Re:  my idea of covering a bike rider's skin with vaseline to block sweat evaporation in order to experience heating by air friction, I forgot that vaseline has some insulating properties which will cause a rise in skin temperature.
Depending on the thickness of the layer of vaseline, we now have a new situation where loss of heat through water evaporation is now zero, while frictional heating is noticeable, and loss of heat through conduction (and radiance) were not considered at the time of the post.
I thought of this idea from remembering how undersea divers prepared for cold water in the days before neoprene suits were invented. They would smear grease or lard over their bodies to insulate and retain bodily heat while working underwater.
If I had access to a sports lab I would like to test these ideas, but I don't.
diverjohn, Sat, 5th Nov 2011

Interesting idea of adding a wind barrier (I think I'd just put on a windbreaker coat).  Certainly if you are working hard, you will generate more body heat.  When I had a bicycle commute over a big hill, just a windbreaker would be enough to keep me warm even on the coldest of days.

If you read the Podcast Page, Holger suggested going about 480 MPH to overcome temperatures of 17°C .  But... perhaps that is a high estimate.

You wouldn't have to bring the temperature up to 98.6°F to experience heating, if you could have a barrier that would prevent sweat loss and some conductive loss.  Perhaps you could just bring the temperature up to 70 or 80°F which would be warmer than the ambient temperatures.

If the temperature was 99°F outside, then in theory, any movement would generate heating.  However, again, the movement of air will help with evaporation, so it wouldn't necessarily feel warmer. CliffordK, Sat, 5th Nov 2011

From what I have noticed things start to change as you enter mach 2.  the temperature rises due to the 'friction' as to where it does make a difference raising the temp rather than cool because it is more of a 'force' and becomes a friction rather than the cooling effect everyone sees on a normal day basis. An example would be when you rub your hand on a carpet.  You can feel the heat right?  Same thing occurs when you are flying at mach 2 considering the speed you are traveling at.  Hope this helps if you haven't already found out. swadewade8, Sat, 12th Nov 2011

I just joined today ...... so don't throw rotten eggs if I make a fool of myself with my first contribution.

Don't forget that Vaseline is a Lubricant, so that might bugger up your Wind FRICTION calculations. Dr Graham, Wed, 30th Nov 2011

May I add an alternative to racing down the highway at 200km/h in a cabrio, naked and covered in vaseline, ie. Get a scuba tank(fulll) and attach a hose to the valve.  Hold the hose opening close to your forearm, and open the valve slowly. Stop when the skin starts peeling off.

Should you feel heat at any moment during the experiment, measure the airspeed through the hose with a wind meter. Ok this idea is possibly not all that accurate, but it may give you an idea on which you can deviate. Stephen Brooke, Tue, 20th Dec 2011

I though heat generated while experiencing drag came from the compression of air molecules in front of the moving body, not just friction between air molecules and skin molecules. hakonmarcus, Thu, 20th Dec 2012

ok but what if the effect desired isn't speed but certain amount of cooling lets say -100c and you had a skin of metamaterial on the bird. Trevor Wilson, Tue, 24th Sep 2013