Calculating Hot Air Balloon Volume & Lift

Click For Summary
SUMMARY

The volume of a hot air balloon is calculated using the formula V = ((4/3)πR³/2) + (1/3)πh(R² + r² + Rh), resulting in a volume of 2956.24 m³ for a balloon with a radius (R) of 9m, height (h) of 15m, and base radius (r) of 1m. The lift force (F) is determined by the equation F = mg - 7350 N, where m is the mass of the balloon (750 kg). The calculations must consider the temperature constraints, specifically that the internal air temperature cannot exceed the external air temperature by 100 degrees Celsius.

PREREQUISITES
  • Understanding of fluid dynamics and buoyancy principles
  • Familiarity with thermodynamics, specifically gas laws
  • Knowledge of mathematical calculations involving volumes and forces
  • Basic understanding of hot air balloon mechanics
NEXT STEPS
  • Research the ideal gas law and its application in buoyancy calculations
  • Explore advanced thermodynamic principles related to hot air balloon operation
  • Learn about the effects of altitude on air pressure and temperature
  • Investigate safety regulations regarding maximum temperature limits in hot air balloons
USEFUL FOR

Aerospace engineers, hot air balloon operators, physics students, and anyone interested in the principles of buoyancy and thermodynamics in aviation.

Desperate
Messages
1
Reaction score
0
Homework Statement
We have to make a hot air balloon that can rise up to 5km and bring up 4 people. In total, the balloon weight is 750 kilogrammes. We cannot exceed the temperature of the air inside by 100 degrees C. We have to find how the temperature of air must change in order for the balloon to maintain a constant rising speed.
Relevant Equations
Fl = V (ρc - ρh) ag
Volume of hot air ballon
V=((4/3 pi R^3)/2) + (1/3 pi h (R^2 + r^2 + Rh) = 2956.24 m3

Balloon:
R=9m
h=15m
r=1m

m = 750 kg
H = 5000m
T = 373 K
p1 = 101300 Pa
p2 = 50650 Pa
M(air) = 0.029 kg/mol
F = mg - 7350 N
 
Physics news on Phys.org
You need to show more of an attempt at working this out. Also, "We cannot exceed the temperature of the air inside by 100 degrees C" is an ambiguous statement. Please clarify.
 

Similar threads

What helium mass in a balloon to make it bouyant in air?
  • · Replies 12 ·
Replies
12
Views
2K
Calculating the Radius of a Hot Air Balloon to Withstand a Load of 300 kg
  • · Replies 2 ·
Replies
2
Views
2K
How Does Temperature Affect the Lifting Capacity of a Hot Air Balloon?
  • · Replies 18 ·
Replies
18
Views
7K
Calculating Air Density and Temperature in a Hot Air Balloon
  • · Replies 6 ·
Replies
6
Views
8K
Is Exponential Form Better for Balloon with Inserted Load Calculation?
  • · Replies 170 ·
6
Replies
170
Views
8K
How Hot Must the Balloon Air Be for a 1000kg Lift?
  • · Replies 13 ·
Replies
13
Views
2K
How Hot Must the Air in a Balloon Be to Lift a Given Mass?
  • · Replies 7 ·
Replies
7
Views
4K
Thermodynamics - Hot-air balloon
  • · Replies 13 ·
Replies
13
Views
7K
Calculating Mass Needed to Ground Hot Air Balloon
  • · Replies 3 ·
Replies
3
Views
2K
Modeling a kongming lantern (sky lantern)
  • · Replies 6 ·
Replies
6
Views
2K