# Modelling flight time

My latest project is building a small, fast, 250-class quadcopter. Since it’s designed to be light and agile, keeping weight down is an essential part of the build. A lot of the total weight (~1/4)  of the quad comes from the battery, so choosing the right size is a major decision.

I decided to model the flight time that different batteries would provide, based on their

• Weight
• Capacity.

Since the current drawn by the motors would be directly determined by the weight of the quad, I needed to find how much current my motors would pull for a given amount of thrust. Of course, this is not a linear relationship, so I used a thrust table for the motors I am using to plot some points in GeoGebra, then created a quadratic function to fit them.

Next, I made a spreadsheet which takes a weight and capacity of a given battery, and calculated the flight time. It is available to view here.

The gist is:

• Find total weight
• Find thrust needed per motor (hovering)
• Find thrust needed per motor (if tilted at a certain angle)
• Divide this thrust by a constant, determined by how smooth/aggressive the flight is (~0.95 for smooth flying, ~0.5 for acrobatic flying)
• Use the Current-Thrust model to  find the current supplied to the motor to sustain this thrust
• Multiply this by 4 to find the total current
• Using this current, and the battery’s capacity, calculate the flight time in minutes.

I will be interested to compare the predicted times with my actual flight times once I’ve finished the build.