$$R = \frac{aM}{g\,c_T}\cdot\frac{L}{D}\cdot\ln\!\left(\frac{W_1}{W_2}\right)$$

Equation 1 · Technological Evolution

Flight at the Energy Floor: Transport Selection to 2100

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Aircraft range is not a free parameter; it is fixed by a single classical relation once cruise speed, aerodynamic efficiency, and fuel fraction are set. In its standard Mach-number form, the range an aircraft can fly in cruise is: $R = \frac{aM}{g\,c_T}\cdot\frac{L}{D}\cdot\ln\!\left(\frac{W_1}{W_2}\right)$. where a is the local speed of sound, M is cruise Mach number, g is standard gravity, $c_T$ is thrust-specific fuel consumption, L/D is the lift-to-drag ratio, and $W_1$ and $W_2$ are the aircraft’s weight at the start and end of the cruise segment [ 1 ] . Three of those four factors — speed, engine efficiency, and aerodynamic efficiency — are where a century of aeronautical engineering has already done most of its work and where further gains now…

Meanings in this article

• $a$: the local speed of sound.
• $M$: cruise Mach number.
• $g$: standard gravity.
• $c_T$: thrust-specific fuel consumption, L/D is the lift-to-drag ratio, and $W_1$.
• $D$: the lift-to-drag ratio, and $W_1$.

Equation guide → · Article →