Variables

$$M _0 = \text{freestream Mach number}$$

$$T _0, P _0 = \text{ambient static temperature and pressure}$$

$$\gamma = \text{ratio of specific heats ($\approx 1.4$)}$$

$$R = \text{specific gas constant}$$

$$c_p = \text{specific heat at constant pressure}$$

$$\pi_d, \pi_c, \pi_b, \pi_n = \text{total pressure ratios across diffuser, compressor, burner, nozzle}$$

$$\eta_c, \eta_t, \eta_n, \eta_d = \text{isentropic efficiencies}$$

$$f = \text{fuel-to-air mass ratio}$$

$$\dot m_a = \text{air mass flow rate}$$

$$h_{PR} = \text{lower heating value of fuel}$$

$$A_e = \text{nozzle exit area}$$

$$V_0 = \text{freestream velocity}$$

$$V_e = \text{exit velocity}$$

ideal turbojet cycle

Intake / Diffuser

Intake Temperature
$$T_{t0} = T_0 \left( 1 + \frac{\gamma-1}{2} M_0^2 \right)$$

Intake Pressure
$$P_{t0} = P_0 \left( 1 + \frac{\gamma-1}{2} M_0^2 \right)^{\gamma/(\gamma-1)}$$

After intake temperature
$$T_{t2} = T_{t0}$$

After intake pressure
$$P_{t2} = \pi_d \, P_{t0}$$

Static temperature after deceleration
$$T_2 = \frac{T_{t2}}{1+\frac{\gamma-1}{2}M_2^2}$$

Compressor / Fan

Ideal isentropic total-temperature ratio
$$\left( \frac {T_{t3}}{T_{t2}}\right) _\text{isentropic} = \pi_c^{(\gamma-1)/\gamma}$$

Total-pressure ratio
$$\pi_c = \frac{P_{t3}}{P_{t2}}$$

Total temperature after compressor
$$T_{t3} = T_{t2} \left[ 1 + \frac{1}{\eta_c} \left( \pi_c^{(\gamma-1)/\gamma} - 1 \right) \right]$$

Compressor power required (shaft power, W)
$$\dot W_c = \dot m_a \, c_p (T_{t3} - T_{t2})$$

Burner

Pressure drop in burner
$$P_{t4} = \pi_b \, P_{t3}$$

Energy balance to set turbine-inlet temperature. Fuel-air ratio:

$$f = \frac{c_p (T_{t4} - T_{t3})}{\eta_b h_{PR}}$$

turbine

$$T_{t5,\text{ideal}} = T_{t4} - \frac{T_{t3}-T_{t2}}{1+f}$$

$$T_{t5} = T_{t4} - \frac{T_{t4}-T_{t5,\text{ideal}}}{\eta_t}$$

$$\dot W_t = (1+f) \dot m_a \, c_p \, (T_{t4} - T_{t5})$$

nozzle

$$\frac{P_{t5}}{P_e} = \left(1+\frac{\gamma-1}{2}M_e^2\right)^{\gamma/(\gamma-1)}$$

$$\frac{T_{t5}}{T_e} = 1+\frac{\gamma-1}{2}M_e^2$$

$$V_e = M_e \sqrt{\gamma R T_e}$$

Thrust

$$F = \dot m_a \left[ (1+f)V_e - V_0 \right] + (P_e-P_0) A_e$$

$$F_s = \frac{F}{\dot m_a} = (1+f)V_e - V_0 + \frac{(P_e-P_0)A_e}{\dot m_a}$$

$$\dot m_f = f \dot m_a$$

$$\mathrm{TSFC} = \frac{\dot m_f}{F}$$

$$\mathrm{TSFC}_{\mathrm{kg/(kN\cdot h)}} = 3600 \frac{\dot m_f}{F/1000}$$

Fan Temperature
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Fan Pressure
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Compression Temperature
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Compression Pressure
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Combustion Temperature
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Combustion Pressure
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Expansion Temperature
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Expansion Pressure
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Compressor Power
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Turbine Power
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Compressor Power tfa
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Turbine Power tfa
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Compressor Power Other
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Critic Pressures Ratio
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Pressures Ratio
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Choking Pressure
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Choking Temperature
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Choking Speed
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Choking Density
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

No Choking Pressure
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

No Choking Temperature
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

No Choking Speed
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

No Choking Density
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Fuel Air Ratio Efficiency
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Jet Nozzle Area
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Thrust
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Specific Thrust
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Fuel Flow
$$\begin{equation*}\mathtt{\text{TSFC = 3600*m\_f/thrust}}\end{equation*}$$

Thrust Specific Fuel Consumption
$$\frac{1}{6}$$