The Question: Let’s go back to our AIRBUS 330-300. Its Operating Empty Weight (OEW) is about 129,400 kg (285,300 lb). Recall that our thrust is 2 times 300,000 N. What is the acceleration of an empty (!) airplane at full thrust?
The Answer:
This is a simple application of the popular form of Newton’s Second law, which we’ll have to rearrange in order to isolate the acceleration:
The units here are a little tricky. 1 N/kg is equivalent to 1 kg m/s. I’ll tell you such things when they happen.
Is that a lot? Let’s look at it two ways. First, ask Mr Google again for the conversion of acceleration. You might have to dig a little for that. If you do you’ll find that:
Notice, that the units of acceleration are different, but the same form: length per time per time. Our airplane’s acceleration results in an increase in speed of 10 mph every second. That’s a lot. Think of being in your car moving at 20 mph. Press on the accelerator and start counting in your head 1 potato, 2 potato, 3 potato…and so on and watch the speedometer increase 30, 40, 50…and so on each second. That’s moving right along.
We could also reach back to our definitional formula for average acceleration and ask how fast we’d be going at that acceleration if we went down the runway for one minute, 60 s.
Do you have a feel for how fast that is? Me neither. So we’ll ask Mr Google and learn that
Okay. That’s really moving right along and too large for a handful of reasons. First, the mass above is for an empty airplane. The full-loaded AIRBUS 330-300 would be twice that massive. Second, full thrust is not used, even at take-off—this is called derated thrust takeoff. And finally, there’s considerable friction from the air and rolling and so the actual thrust is much less efficient than the rating.