The picture below rapresents a block transfer function of a motor. It can be any kind of it, let we suppose it's about brush DC motor with permenent magnet. Any other type shall be transformed in the d,q coordinate system. For PMSM or BLDC this is done with Park and Clarke transformation. The d-component is the excitation, a permanent magnet. The q-component is related to the torque, in DC brush motor is the armature component.

Thus, \$u_q\$ is the armature voltage, \$R_q, L_q\$ are resistance and inductivity of the armature, \$k_\Phi\$ is the flux constant (kv in your case, but with different units), \$M, M_L\$ is motor torque and load torque, \$J\$ is the moment of inertia, \$F\$ is the friction constant, \$\Omega\$ is the angular speed, \$\Theta\$ is the angle of the motor, \$U_i\$ is the back EMF voltage.

For better understanding you should look for Field oriented control, where you will find how a multi phase machine is transformed into a d,q model (brush DC motor with separate excitation), then all the copmutation is the same as DC motor.

EDIT:
The block diagram is reararanged in a equation using the property of closed loop rearangement. Let the open loop blocks rapresent \$G_1(s)\$ and the feedback path \$H(s)\$, which in our case is \$k_\Phi\$. The equivalent transfer function of the closed loop is: $$ G(s)=\dfrac{G1(s)}{1+G1(s)\cdot H(s)}$$

This yields the transfer function of speed vs. voltage:

$$ \dfrac{\Omega(s)}{u_q(s)} =\dfrac{\dfrac{k_\Phi}{L_qJ}}{s^2 + s\dfrac{R_qJ+L_qF}{L_qJ}+\dfrac{R_qF+k_\Phi^2}{L_qJ}} $$

$$ \dfrac{\Omega(s)}{u_q(s)} =\dfrac{{k_\Phi}}{s^2L_qJ + s{R_qJ+L_qF}+{R_qF+k_\Phi^2}} $$ You may see it is a second order system.

EDIT: from Anton Skuric's notes: Corrected formula with missing F. The formula is valid for DC motor. For BLDC and PMSM the \$k_v\$ and \$k_i\$ are not equal, thus \$k_{\Phi}\$ should be split to \$k_v\$ and \$k_i\$.

EDIT: Separate voltage constant \$k_v\$ and torque constant \$k_i\$ instead of the same \$k_{\Phi}\$

$$ \dfrac{\Omega(s)}{u_q(s)} =\dfrac{{k_i}}{s^2L_qJ + s{R_qJ+L_qF}+{R_qF+k_v\cdot k_i}} $$

• The simple answer is that a Dc motor has an RPM that is proportional to V until a non-linear aerodynamic load such as your prop, disturbs the transfer function with a non linear reduction in speed vs V,
• then it becomes a more linear function of lift proportional to current (or torque transferred to lift vs current,
  • with some eddy current losses due to air coupling losses and choice of prop.
  • just as impedance matching is critical in transmission lines of RF, you want to choose the Prop to match the mechanical impedance of the prop to the mechanical impedance of the motor torque at the ideal RPM to obtain maximum HP or lift . Further details are beyond the scope of this question.

Then the differential average current between prop motors determines the tilting force. Motor current translates to torque while voltage translates to "no load" RPM. Actual transfer function requires monitoring V, I and RPM to know lift. which can be calibrated on the bench, then you can choose prop for high payload weight or high speed. Motor heat loss rises with both V and I and motor T accelerates wear, while bearing wear rises exponentially with RPM

• RPM/V: 2480KV. means with no prop , 2480 RPM per Volt

Here is a clever guy who uses his wife's kitchen scale to measure thrust which correlates with motor current using throttle to control speed.

http://www.rcgroups.com/forums/showthread.php?t=2168392

Here are some specifications for a similar motor

Here are some Prop specs where Motor power and current are the key indicators for max thrust for 1st order approximations for this motor and various props