Tips For Making Flying Lanterns:
When making a hot air balloon, the diameter proportion of the mouth and bottom should be smaller than 0.7. Otherwise, it will lead to the escape of hot air.
Pair >= G + Fdown
P is the absolute pressure of the gas, in Pa
ρ is the density of the gas, in kg/m3
R is the gas constant, in Joules/kg.K
T is the absolute temperature of the gas, in Kelvins (K)
So we can get ρRT = mg + ρ1RT1
Normal atmospheric pressure is approximately 101,300 Pa
The gas constant for dry air is 287 Joules/kg.K
The air inside the envelope is typically heated to an average temperature of about 100 degrees Celsius, which is 373 K
Substituting the above three values into the Ideal gas law equation and solving for ρ we get ρ = 0.946 kg/m3. This is the density of the heated air inside the envelope. Compare this to normal (ambient) air density which is approximately 1.2 kg/m3.
So the format can equal to R= mg/(ρT - ρ1T1)
But they all sound bullshit to us so we did 'trial and error' instead. We started the process with creating a tissue paper lantern.
After 10 minutes of holding up for it to take off, it did not want to fly but stick to the ground like magnets. The first lantern totally failed.
Comparing the tissue paper with the original paper that comes with the flying lantern from the shops, the tissue paper seemed to be light enough for the lantern to be taken off. However, it failed due to lack of accuracy and proximity of the lantern so hot air could not build up inside the balloon sufficiently. The lantern may have been too small as well.