Air Pressure, Altitude, Balloons and Rockets

Weather Balloon BurstAir Pressure and how it Affects Balloons and Rockets

By Robert Brand

Rockets

One of the big issues for rockets flying to space is the air pressure it must climb through. As a rocket climbs it gets faster and has to push more air out of the way. As it goes higher the air thins and you can see from the table below that it is exponential. Have a look at the 1/100th  fraction of one atmosphere below and you will see that the atmosphere is 1% of sea level. The change is not linear. The atmosphere thins to a tiny percentage at twice that height, but at half the height it is 10% of the sea level pressure.

NASA says: The velocity of a rocket during launch is constantly increasing with altitude. Therefore, the dynamic pressure on a rocket during launch is initially zero because the velocity is zero. The dynamic pressure increases because of the increasing velocity to some maximum value, called the maximum dynamic pressure, or Max Q. Then the dynamic pressure decreases because of the decreasing density. The Max Q condition is a design constraint on full scale rockets.

fractionof 1 atmosphere (ATM) average altitude
(m) (ft)
1 0 0
1/2 5,486.3 18,000
1/3 8,375.8 27,480
1/10 16,131.9 52,926
1/100 30,900.9 101,381
1/1000 48,467.2 159,013
1/10000 69,463.6 227,899
1/100000 96,281.6 283,076

The Falcon9 reaches the speed of sound at 1 min 10 sec into its flight and then reaches Max Q just 8 to 13 seconds later depending on speed,and air pressure variables. Unlike airplanes, a rocket’s thrust actually increases with altitude; Falcon 9 generates 1.3 million pounds of thrust at sea level but gets up to 1.5 million pounds of thrust in the vacuum of space. The first stage engines are gradually throttled near the end of first-stage flight to limit launch vehicle acceleration as the rocket’s mass decreases with the burning of fuel.

Want to know more? This is not full of maths, just some fun stuff about Max Q and reaching orbit.

Balloons

Well for balloons we have a different issue. Balloons have to displace their weight in gas in the atmosphere and that includes displacing enough gas for the weight of the payload too.

Rate of Climb - Fall vs TimeThe climb to maximum altitude for the most part is linear. I discovered this when analysing the stats from my first balloon flight. It was linear until it reached the point that the balloon exploded. If you launch a balloon that does not explode, it will slow its climb and then float. My best guess is that as the climb becomes more difficult due to the air thinning thus and thus the displaced gas is getting closer to the weight of the balloon and payload, but the air resistance is getting less. The size of the balloon is also increasing with height and has to push away a greater volume of air to climb, but the number of air molecules in the increased mass is way less. All up it produces a fairly linear climb. The graph (left) from uplift-1 shows he linear climb and the exponential fall with the parachute deployed. For the parachute, the air gets thicker as it falls and thus slows more as the altitude decreases. Note the initial glitch was caused by a strong thermal just as we let go of the balloon. Once out of the thermal the climb was very linear. It is obvious when the balloon burst.

Altitude and Air PressureAnother view of th same data is shown on the left from UpLift-1’s flight. Note that the rate of climb is linear, but increasing slightly. This would be affected by balloon size and fill amount. The rate of climb may be fast, slow or medium, but that will also change the rate of change of the volume. Not all graphs are the same, but they tend to be similar. Note also that the size of the parachute needs to change with the weight of the payload. The ideal speed for the average payload would be about 5mto 6m per second at the landing altitude, thus landing at Denver, Colorado, USA will require that you make the parachute a little bigger since it is nearly 2Km above sea level and the air is noticeably thinner.

There are good fill charts on the web allowing you to calculate the size of balloon and the amount of Helium or Hydrogen to determine the altitude at which the balloon will explode. More on that another time. The picture at top of page is a weather balloon exploding at altitude.

All up, air pressure can destroy a rocket if its speed is too great and it will destroy a weather balloon if the air pressure gets too low. Both rely on understanding the effects of air pressure, but the dynamics are totally different.

Too finish off the post here is a video of a balloon burst. They are spectacular, especially as the balloons grow to a huge diameter and fill the screen of most wide angle GoPros!: