Ideal DDWFTTW Cart Force and Power Calculator

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Pwind = Wind Power (IFOR=ground) =		->	->	->
Fwind = Wind Force (IFOR=ground) =		->	->	->
Vwind = Wind velocity (IFOR=ground) =		ρ = Density of Fluid =		S = Area of rotor disc =
Vcart = Cart velocity (IFOR=ground) =		= n		D = Diameter of disc =
ΔV = Air velocity change due to prop =		= Δ
Δmax = Value of Δ which maximizes Fnet =				Start n =
V1 = Inlet air velocity (IFOR=cart) =		= i		Stop n =
V2 = Outlet air velocity (IFOR=cart) =		= o		n increment =
V = Prop disk air velocity (IFOR=cart) =		= v		Timing interval (ms) =
A1 = Area of control volume inlet =		= a1
A2 = Area of control volume outlet =		= a2
MDOT = Mass flow rate (IFOR=cart) =			->	->
Pprop = Pin=(Fg * Vcart) = Pout=(Ft * V) =		= CPprop	->	->	->
Ft = Thrust force of air acting on propeller =		= CFt	->	->	->
Fg = Force of ground acting on wheel =		= CFg	->	->	->
Fnet = Net force (Ft - Fg) =		= CFnet	->	->	->
Pnet = Net Power (Fnet * Vcart) =		= CPnet	->	->	->

"When the fields are green, the data is clean!"

Every Compute button press recalculates all parameters.
Entering just a number without units uses the last active units.
Entering just units without a number converts the value to those units.
When you change a value, it's text background color is set to light blue.
To see the available (case-sensitive) units, hover over the text fields on the left.
Most parameters have two flavors; the first has units and the second is dimensionless.
Dimensionless velocity parameters are normalized with respect to Vwind.
Dimensionless force parameters are normalized with respect to Fwind.
Dimensionless power parameters are normalized with respect to Pwind.
EQ16 determines the Δ value that maximizes Fnet for a given n.
You can lock in the optimal Δ value by checking the checkbox next to Δmax.
You can enter commands into any text box having form: COMMAND=PARAMETER. See below.
You can change the units of all parameters - e.g. UNITS=METRIC, UNITS=IMPERIAL.
You can change units for all parameters having common units - e.g. FORCE=N, SPEED=m/s.
You can multiply or divide a value by a number - e.g. *4, /3.14.
You can enter a rational number using integers - e.g. 4/3, 16/27.

Equations used:

EQ1: Pwind = 1/2 * ρ * S * Vwind3
EQ2: Fwind = 1/2 * ρ * S * Vwind2
EQ3: n = Vcart / Vwind
EQ4: Δ = (V2 - V1) / Vwind
EQ5: V1 = Vcart - Vwind
EQ6: V2 = V1 + ΔV
EQ7: V = (V1 + V2) / 2
EQ8: A1 = S * V / V1
EQ9: A2 = S * V / V2
EQ10: MDOT = ρ * S * V
EQ11: Pprop = 1/2 * ρ * S * Vwind3 * ( 1/2*Δ3 + (2*n - 2)*Δ2 + (2*n2 - 4*n + 2)*Δ )
EQ12: Ft = 1/2 * ρ * S * Vwind2 * ( Δ2 + (2*n - 2)*Δ )
EQ13: Fg = 1/2 * ρ * S * Vwind2 * (1/2*Δ3 + (2*n - 2)*Δ2 + (2*n2 - 4*n + 2)*Δ) / n
EQ14: Fnet = 1/2 * ρ * S * Vwind2 * (-1/2*Δ3 + (2 - n)*Δ2 + (2*n - 2)*Δ ) / n
EQ15: Pnet = 1/2 * ρ * S * Vwind3 * ( -1/2*Δ3 + (2 - n)*Δ2 + (2*n - 2)*Δ )
EQ16: Δmax = 2/3 * (2 - n + (n2 - n + 1)1/2)


Description of Dimensionless parameters:

n = Velocity of cart (IFOR=gnd) = Vcart/Vwind
Δ = Change of air velocity (IFOR=any) = ΔV/Vwind = o - i
i = Velocity of air entering control volume inlet (IFOR=cart) = V1/Vwind = n - 1 = o - Δ
o = Velocity of air exiting control volume outlet (IFOR=cart) = V2/Vwind = i + Δ
v = Velocity of air passing through rotor disc (IFOR=cart) = V/Vwind = i + Δ/2 = o - Δ/2
a1 = Area of control volume inlet = A1/S
a2 = Area of control volume outlet = A2/S
CPprop = Coefficient of power passing from propeller to air (IFOR=cart) = Pprop/Pwind
CFt = Coefficient of thrusting force of air acting on propeller = Ft/Fwind
CFg = Coefficient of braking force of ground acting on rear wheel = Fg/Fwind
CFnet = Coefficient of net force = Fnet/Fwind = (Ft - Fg)/Fwind = CFt - Cfg
CPnet = Coefficient of net power (IFOR=cart) = Pnet/Pwind = CFnet * n