Well, not really the most appropriate/perfect subject name but I wanted to get the attention of the folks out there more learned than me in the study of the variables of air.
A coworker recently asked if rockets fly "better" (more efficiently) in the winter than summer. I responded that I didn't believe that they do but after thinking about it I've decided that I really don't know that for certain.
My negative response was in all likelihood directly related to his assertion that they must because hot air balloons fly in cold weather with less propane than is used in the summer. I countered by saying that it is probably easier to get the air in the balloon less dense than the cold ambient winter air using the same sized "heater" on a given balloon so the buoyancy of the bag of air is probably more dramatic in the winter. (And I wonder that if on a given flight in winter you'd really use less fuel heating the air in the balloon than on the same flight in the summer because of having to re-heat the air more often. Anybody know the answer to that?)
The discussion then went on to airplanes. I understand that cold air creates greater lift because it is more dense. Thus more air molecules pass over the airfoil at a given speed than do in warm air thereby generating more lift. This greater lift capacity of air is also true at lower elevations due to its increased density.
I believe what I've said above is correct - feel free to correct me if I'm wrong.
Now for the rocket related question: Is there anything in the flight of a rocket that increases, is better or more efficient in cooler than rather than warmer ambient air?
The engines get more thrust against air that is more dense. Also, the stabilizing surfaces have more effect in air that is more dense. It is true that drag will also increase in the forward surfaces, but in practice, it doesn't not ruin the gains from the other two.
Someone with more "rocket science" background than I can probably post some formula(s) and a better explanation.
pressure thrust (a function of the pressure differential between the inside of a motor and atmospheric pressure) decreases with increase in external air density
so the rocket would fly slower in colder air
I can't say how significant the effect would be in a temperature range of, lets say, 20 to 110 degrees F (the most extreme temperature conditions I have flown under)
I assume this is the question you were answering. If so, that is incorrect. Humid air is less dense than dry air and reduces vehicle drag. Warmer air can hold more water vapor.
You also get better engine performance due to the denser air. IIRC the Streak Eagle time to climb records were all set in the winter up north in Canada...
If you're talking about altitude, I think not.
Can't speak for Rocksim, but at least pRASP has ambient temperature as one of its variables. Try it and see. [Alas I left my PDA at home today. It's been a rough day without it...]
Bob Kaplow NAR # 18L TRA # "Impeach the TRA BoD" >>> To reply, remove the TRABoD!
The same dense air that makes a airplane get more lift and carry more weight makes a rocket fly less high. It has more drag to over come and the offset from the other factors does not help it much.
To make sure I had not lost my senses, as I have gotten real old since I played with slide rules in the 70s, I opened up rocksim 7.0 and loaded an estes big daddy.
I loaded a D-12-5 and "flew" it at 72 degree, 640 feet ASL. I flew at 80% and 5% humidiy and at 42 and 0 degrees.
The lower temperature flew lower each time.
At 5% at 0 degreess and 5% 72 degrees , the rocket still flew lower at colder temperates, about 15 feet lower.
so at least on a large body rocket this common sense worked.
what about a skiny rocket ?
An appogee blue streak was just loaded and flew on a b6-6. It flew 70 feet lower at 0 degrees 5% humidity then at 72 degree, 5% humidity.
I love simulators,
/ArtU
PS , I now they are not the end all, but they really do help !
That's true with AIR breathing engines like pistons and jets, but rocket motors have their own oxidiser. In air breathing engines, with denser air, you can richen the mixure more and get better ISP on your gas or JET fuel. The Stike Eagle breaths Air.
the rocket motor does not notice the extra air density, cause it's not breathing any. no air intake on my K660 motor I can find, he he..
For once, CT is correct. The ISP of APCP is reduced significantly with lower temperatures. The added drag from higher density colder air will have a lower affect.
Don't bother using a pressure-based altimeter to verify this... temperature has an impact on both the atmospheric model and on the calibration of the sensor & circuitry.
*** WARNING - TECH POST **** I.E. MORE THAN YOU (PROBABLY) WANT TO KNOW:
The lift force of a balloon (F) is a function of its displacement volume (V) and the difference in density between the gas inside and the atmosphere outside:
eqn. 1 F=V*(rho,amb-rho,envel)*g
where rho,amb = the density of the ambient atmosphere rho,envel = the density of the hot air inside the envelope of the balloon g = local gravity acceleration
The hot air inside a hot air balloon has essentially the same composition as the outside air, its just at a higher temperature. How much higher depends on how much lift is required, limited by materials temperature capabilities of course. Air under these conditions is an ideal gas and follows the ideal gas law:
rho = P/(Rm/w*T)
where P = pressure Rm = molar gas constant (this is actually constant, even) w = molecular weight (28.965 g/mole for dry air) T = temperature (absolute, i.e. with respect to absolute zero)
So... replacing the densities in eqn. 1 using the ideal gas law yields:
F=V*(1/Tamb-1/Tenvel)*g*P/(Rm/w)
a little re-arrangement gives us the temperature in the balloon envelope needed to develop the lift force required by the payload:
Tenvel=Tamb/[1-F*(Rm/w)/(P*V*g)]
Convective heat transfer from the balloon envelope to the ambient atmosphere can be characterized by Newton's law of cooling:
Q=h*A*(Tenvel-Tamb)
where Q = heat loss rate h = the convective heat transfer coefficient (approximately constant) A = heat transfer surface area Now, substituting the expression for the required balloon envelope temperature into the convective cooling rate law yields:
Q=h*A*Tamb*x/(1-x) where x=F*(Rm/w)*Tamb/(P*V*g)
If we are using combustion to supply heat to the air in the balloon envelope, then:
Q=mdotf*dhcomb
where mdotf = the fuel mass flow rate dhcomb = the fuel heating value per unit mass (enthalpy of combustion)
Therefore:
mdotf=(h*A*Tamb/dhcomb)*x/(1-x)
The fuel mass flow rate required to stay aloft is directly proportional to the ambient air absolute temperature - it therefore requires less fuel to stay aloft for a given time in cold weather when Tamb is smaller and the displaced air is denser.
QED
Additional observations: It helps to minimize the heat transfer surface area, so don't put ribs or appendages on your balloon - make it a sphere as much as possible. It also helps alot to minimize "x", which is a dimensionless ratio of the lift force developed to the weight of the ambient air displaced by the balloon. You are therefore more efficient by minimizing "x" using a larger balloon since the displaced (i.e. enclosed) volume increases faster than the heat transfer surface area (assuming a spherical balloon). Smaller "x" also lets you get to higher altitude. You would also be better off in a stronger gravity field and/or denser atmosphere, like Jupiter or Venus versus Earth. Nuclear hot "air" balloon, anyone? (if you think getting an LEUP is a pain ...) It will be harder to float a hot air balloon on Mars, though.
This equation shows that another relevant dimensionless quantity in addition to "x" is:
mdotf*dhcomb/(h*A*Tamb)
which is a ratio of heat input rate to a reference heat loss rate. Someone probably has named these dimensionless quantities already, for example "x" should be called something like the Montgolfier number, etc.
Math is great.
Brad Hitch Registered PE, Ohio Cooper Nuclear Station alum
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