Terminus said:I'm just wondering what a curve would look like if the x-axis is the temperature inside a hot air balloon and the y-axis is the diameter (in feet) of the balloon. There's a relation in how many pounds a hot air balloon can lift based on this curve and I'm looking to see what a good balance would be between both x and y to be able to lift 400 pounds into the air.
The curve of a hot air balloon can be described by a parabolic function, specifically a quadratic equation in the form of y = ax^2 + bx + c. The exact coefficients of a, b, and c will depend on the specific dimensions and characteristics of the hot air balloon.
The weight of the hot air balloon will affect the shape of the curve by changing the value of the coefficient a. A heavier balloon will have a higher value of a, resulting in a steeper and narrower curve. On the other hand, a lighter balloon will have a lower value of a, resulting in a flatter and wider curve.
If the hot air balloon is filled with helium instead of air, the curve would be slightly different due to the difference in density between the two gases. Helium is less dense than air, so the balloon would be able to lift more weight and the curve would be slightly flatter compared to a hot air balloon filled with air.
Yes, the shape of the curve can change during the flight of a hot air balloon. This can occur due to changes in temperature, wind conditions, and weight distribution within the balloon. The pilot can also manipulate the shape of the curve by adjusting the amount of hot air or gas in the balloon.
Yes, it is possible to calculate the exact curve of a hot air balloon using mathematical equations and known variables such as weight, gas volume, and temperature. However, the curve may change slightly during the flight due to external factors. Therefore, it is important for the pilot to continuously monitor and adjust the balloon during the flight.