Sizing scenarios and design drivers (student version)

Written by Marc Budinger (INSA Toulouse), Scott Delbecq (ISAE-SUPAERO) and Félix Pollet (ISAE-SUPAERO), Toulouse, France.

The preliminary sizing of UAVs aims at defining the main drone characteristics and selecting the components based on a few sizing scenarios. The sizing scenarios are part of the specification process and may include both transient and endurance criteria, such as maximum rate of climb and hover flight endurance. The final overall design has to consider simultaneously the various sizing scenarios that may impact the components selection through design drivers.

Design drivers

Design drivers are physical factors that influence the design process of a component. For example, the propeller design is driven, among others, by the maximum thrust it can provide.

Table 1 summarizes the main system components.

Exercise 1

For each component, list the main design drivers to be taken into account for the design process. Complete Table 1.

Sizing scenarios

Endurance scenarios, like hover flight need to be taken into account for the selection of the battery endurance and the evaluation of the motor temperature rise. Extreme performance criteria, such as maximum transitory acceleration or maximum rate of climb are fundamental to determine the maximum rotational speed, maximum propeller torque, Electronic Speed Controller (ESC) corner power, battery voltage and power, and mechanical stress.

Exercise 2

For each design driver, list the critical scenarios that need to be taken into account for the component selection. Complete Table 1.

Table 1: Design drivers and sizing scenarios

Components	Design drivers	Sizing scenarios
Propeller	Max thrust	Takeoff
		Climb
Motor
Electronic Speed Controller
Battery
Frame

Equations of sizing scenarios

The purpose of this notebook is to illustrate on an existing drone example the main equations to be taken into account during the sizing. The selected drone is the MK-Quadro drone of Mikrokopter. The technical informations about the MK-quadro drone can be found on the website of MikroKopter company.

Fig. 4 APC MR (Multi-Rotor) propellers

Propellers fundamental equations

Propellers can be described in an ideal manner by the disk momentum theory. The dimensional analysis theory enables to describe with more details the propeller performances thanks to aerodynamic coefficients:

• The thrust: \(T = C_{T,h} \rho \Omega^2 A R^2=C_{T,p} \rho n^2 D^4\) which gives \( = k_{TD} \Omega^2\) for a given propeller and a given diameter

• The power: \(P = C_{P,h} \rho \Omega^3 A R^3=C_{P,p} \rho n^3 D^5 \) which gives the power \(P=k_{PD}\Omega^3\) or the torque \(M = k_{PD} \Omega^2\) for a given propeller and a given diameter

Note

Be carefull, litterature shows 2 notations :

• the propeller notation with n the propeller speed in [rev/s], D the diameter in [m], \(\rho\) the air density in [\(kg/m^3\)]

• the helicopter notation with \(\Omega\) the propeller speed in [rad/s], R the radius in [m], \(A\) the disk area in [\(m^2\)], \(\rho\) the air density in [\(kg/m^3\)]

Exercise 3

Compare the caracteristics of the following APC propellers to those of the MikroKopter MK-Quadro (GWS)

Characteristics	APC Propeller	GWS Propeller
Diameter [inch]	10	10
Pitch [inch]	4.5	4.5
Thrust coef \(C_t\) [-]	0.1125
Power coef \(C_p\) [-]	0.0441
Thrust coef \(k_{TD}\) [\(\frac{N}{(rad/s)^2}\)]		\(1.799.10^{-5}\)
Torque coefficient \(k_{PD}\) [\(\frac{N}{(rad/s)^2}\)]		\(3.054.10^{-7}\)

with: \(1\) \(inch = 0.0254\) \(m\), \(\rho=1.18\) \(kg/m^3\)

D = 10 * 0.0254  # [m] Propeller diameter
rho = 1.18  # [kg/m^3] Air mass volumic (25°C)

# APC coefficients
# Ct=T/(rho * n**2 * D**4) (thrust coef.)
Ct = 0.1125  # [-] Thrust coefficient, propeller notation
# Cp=P/(rho * n**3 * D**5) (power coef.)
Cp = 0.0441  # [-] Power coefficient, propeller notation

Hover flight scenario

The flight conditions in static hover are no forward speed, no vertical speed. This scenario influences in a very important way the autonomy of the vehicle. The thrust generated by propellers have to compensate the global weight of the drone and the load.

Fig. 5 An actuator disk accelerating a fluid flow from right to left (Source: Wikipedia).

Exercise 4

With the given technical informations, calculate the requested thrust for each propeller for a no load hover flight.

Characteristics	MK-MikroKopter drone
Total mass ready to take off	1350 g
Number of propellers	4

# Hover scenario
# ------------
M_total = 1.35  # [kg] mass of the drone

N_pro = 4  # [-] propeller number
D_pro = 2.54e-2 * 10  # [m] propeller diameter

# to be completed

Exercise 5

With the given technical informations of GWS propellers calculate the propeller torque, speed and the mechanical power.

# Propeller characteristics
# -----------------------------

K_TD = 1.799e-5  # [N/(rad/s)^2] thrust coef
K_PD = 3.054e-7  # [N.m/(rad/s)^3] torque coef

# to be compared to the ones calculated with regression
# GWS 10*4.5

D_pro = 10 * 0.0254  # [m] diameter

# Torque and RPM of motors
# -----------------------

# to be completed
#

print("----------------")
print("Propeller speed: %.2f rad/s or %.0f RPM" % (W, W / 2 / 3.14 * 60))
print("Propeller torque: %.2f N.m " % (M))
print("Propeller power: %.2f W " % (M * W))

----------------

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[3], line 19
     12 # Torque and RPM of motors
     13 # -----------------------
     14 
     15 # to be completed
     16 #
     18 print("----------------")
---> 19 print("Propeller speed: %.2f rad/s or %.0f RPM" % (W, W / 2 / 3.14 * 60))
     20 print("Propeller torque: %.2f N.m " % (M))
     21 print("Propeller power: %.2f W " % (M * W))

NameError: name 'W' is not defined

Questions:

Exercise 6

With the following technical informations calculate the motor voltage and current, the autonomy of the drone if we assume an efficiency of 95% for electronic speed controllers (ESC) and a depth of discharge of 80% for the battery.

Component	Characteristic	Value
Motor	Poles pair number	7
Load current	6‐9A (DC)
Max current	10A (DC)
Speed constant Kv	760 tr/min/V
Mechanical power	110 W
Dimensions	28.8 x 29 mm
Max efficiency	76 %
mass	65 g
Resistance	R = 0.26 ohm
Inertia	J= 2.5e-5 kg.m²
Battery	Voltage	LIPO 4S (4*3.7V)
Capacity	3300mAh
mass	329g

# Voltage / current calculation
# -----------------------------

K_T_mot = (1 / 760) * 60 / 2 / 3.14  # [V/(rad/s)] Motor torque coef
R_mot = 0.26  # [Ohm] Motor resistance

# Voltage / current calculation

# to be completed

print("----------------")
print("Motor current: %.2f A " % I)
print("Motor voltage: %.2f V " % U)

# Autonomy of the battery

# to be completed

print("----------------")
print("Battery current: %.2f A " % I_bat)
print("Battery voltage: %.2f V " % V_bat)
print("Autonomy of the battery : %.1f min" % Aut_bat)

----------------

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[4], line 12
      7 # Voltage / current calculation
      8 
      9 # to be completed
     11 print("----------------")
---> 12 print("Motor current: %.2f A " % I)
     13 print("Motor voltage: %.2f V " % U)
     15 # Autonomy of the battery
     16 
     17 # to be completed

NameError: name 'I' is not defined