1. PURPOSE / DESCRIPTION

To give a guideline on how to use the energy savings and predicted terminal velocity calculator for quads (Excel file) at different angles.
- This is useful if you have followed the EPs and ETPs for running wind tunnel simulations on desired bodies. This procedure will follow an example with the BIONX drone simulations.
- This procedure does assume you have decent knowledge of Excel.
File name = “Quad Simulation Data and Calculator” (The calculator itself has comments to guide usage.)

2. General Layout

Name	Units	Definition	Notes
Weight	N	weight of craft including the wing
Cl (wings)		wing’s coefficient of lift	It may be best to do a separate 3D simulation of the wing to obtain accurate Cl and Cd values.
Cd (wings)		wing’s coefficient of drag
Wing Chord	m	wing chord length	Input average chord length if the wing is not rectangular.
Wing Span	m	wing span
Wing Area	m²	wing planform area	For rectangular wings it uses spanarea formula, but for non-rectangular, you must input a flat calculated value for the planform area*.
Drone Ref Area	m²	drone reference area	This is the area input in Fluent’s Reference Values section used to calculate Cd and Cl values for the body. If you used symmetry for simulation, make sure to double that area for this input.
Air density	kg/m³	density of air at 288.16 °C
Air viscosity	kg/(m*s)	dynamic viscosity of air at 288.16 °C
Area Ratio		Wing Area / Drone Ref Area

Craft Cd and Cl
- These values should can be found by running simulations on just the body without the wing at varying angles of attack.
- The example calculated uses results from simulations on the BIONX body, as shown below:
- By creating best fit curves onto the obtained coefficients, you can use them as formulas to interpolate from 0 to 90 degrees in the table. So you will have to change the formula of the cells under Craft Cl and Craft Cd to fit the model.
  - Make sure to have enough digits in the formula’s coefficients, as by default excel will provide few enough digits to give completely different numbers.

Run simulation on the desired wing through fluent or obtain experimental data to find accurate wing Cl and Cd values.
Run simulations on the quad body at different angles of attack (check out EP-702,703,705)
- Obtain Cd and Cl on the body, make sure to keep the reference area is constant throughout the various angles.
- If you use symmetry for the simulation, make sure to double the reference area for the Drone Ref Area input.
- Plot the coefficients against angle of attack, fit a line or a curve on the plots, and obtain the equation. Make sure to have a sufficient number of decimal digits within the equation.
Input all information gathered
- Change the formula of Craft Cd and Craft Cl to match what you have obtained from your simulation results. (The coefficients can be constant as well: just make sure to input a constant value for all cells in those columns.)
- Look to the right of the inputs to see the minimum energy ratio, the required thrust, the angle for that ratio, the terminal velocity, and required velocities for Re # 50,000 and 100,000.
Check that column Vt (m/s) is equal to column Vt (w/Cl).
- Vt (m/s) is calculated using combined Cd from the chart while Vt (w/Cl) is calculated using the combined Cl from the chart. If these values do not match, you may have made an error putting in the formulas or values.