What's the acceleration and absolute minimal RWY length for an A320 during take-off? TL;DR: An A320 takeing-off with full thrust is able to reach $V_{TO}$ (77 m/s) in only 26 seconds and in as few as ~ 1.000 metres. Is that really true?



Last time I traveled with an A320 I was again impressed by the acceleration during takeoff. I think it's not outstanding (compared to others) but nonetheless impressive. A cause might be that passengers are somehow exposed to the powers and cannot influence it. But I enjoyed it and it made me doing some calculations.

I gathered the following data:


usual take-off speed $V_{TO}=150$ knots (source)
required runway length $2000 \text m$ (source)
max. thrust per engine $\approx 120 \text{kN}$ (source)
MTOW $78 \text{tons}$ (source)


For constant acceleration along a path the following rules apply:

$$\left.
\begin{array}{}
s = \frac{1}{2} at^2 &amp; \Leftrightarrow &amp; t = \sqrt{ \frac{2s}{a} } \\
v = a \cdot t        &amp; \Leftrightarrow &amp; t = \frac{v}{a}
\end{array}
\right\}
\Rightarrow
a = \frac{1}{2}\frac{v^2}{s}$$

With the data from above this gives an acceleration from 0 to 100 km/h (or 62 mph or 28 m/s) in approximately 18.5 seconds and about 52 seconds for reaching the take-off speed. That sounded a bit lame compared to my 100hp station wagon.

So I investigated further, this time from Newton's point of view, $F=ma$, which gives an acceleration of $a = \frac{2 \cdot 120.000 N}{78.000 kg} \approx 3 \frac{m}{s^2}$. That gives 0…100 km/h in about 9 seconds. This far better coincides with my gut feeling as a pax.

But my second approach, $a \approx 3 \frac{m}{s^2}$, also resulted in the following conclusion and question: 

An A320 takeing-off with full thrust is able to reach $V_{TO}$ (77 m/s) in only 26 seconds and in as few as ~ 1.000 metres. Is that really true? I was amazed at this because they all say the required RWY length is twice as long.
At takeoff weight of 78.9 tonnes and -20°C temperature (best case scenario), the A320 needs 2,250 metres (7,400 feet). (This includes the distance to reject a takeoff.)

As for the forces, you forgot to take into account the aerodynamic drag and rolling friction, both will slow down the acceleration.



This PDF from Virginia Tech explains the forces at work and the equations needed.