Friday, August 10th, 2007...1:23 pm
Notes to myself — calculating lift of helium, hot air
A 100-foot-diameter balloon can lift 33,000 pounds! Here is how you can figure out the lifting capacity of the helium in a spherical helium balloon:
1. Determine the volume of the balloon. The volume of a sphere is 4/3 * pi * r3, where r is the radius of the balloon. So first determine the radius of the sphere (the radius is half the diameter). Cube the radius (multiply it by itself twice: r*r*r), multiply by 4/3 and then multiply by Pi. If you are measuring your balloon in feet, that gives you the volume of the balloon in cubic feet.
2. One cubic foot of helium will lift about 28.2 grams, so multiply the volume of the balloon by 28.2.
3. Divide by 448 — the number of grams in a pound — to determine the number of pounds it can lift.
So, for example, a 20-foot balloon has a radius of 10 feet. 10* 10 * 10 * 3.14 * 4/3 = 4,186 cubic feet of volume. 4,186 cubic feet * 28.2 grams/cubic feet = 118,064 grams. 118,064 grams / 448 grams per pound = 263 pounds of lifting force.
Although not used much anymore, hydrogen balloons were once quite popular. Hydrogen weighs just 0.08988 grams per litre.
If you heat the air inside the balloon 100 degrees F hotter than the outside air temperature, then the air inside the balloon will be about 25 percent lighter than the air outside the balloon. So a cubic foot of air weighs about 35 grams at 32 degrees F. A cubic foot of hot air at 132 degrees F will weigh 25 percent less, or about 26.5 grams. The difference is 8.5 grams or so. So a hot air balloon has to be much bigger to support the same weight, but it will float because hotter air is lighter than cooler air.
Leave a Reply
You must be logged in to post a comment.