How can an airplane descend faster than a free-falling roll of toilet paper?

Watching this video, I was wondering, does the Toilet paper have this much lift, because I think the descent speed of the Airplane is not that much?

• I don't think that a parachute-plane can catch up with a person in free-fall?
• Can somebody explain me physical how this maneuver works?
• powered dive (nose is down) and a high-drag object -> kinda obvious Commented Nov 6, 2014 at 16:18
• Ahhhh, there's nothing quite like littering from however many thousand feet. Commented Nov 6, 2014 at 16:28
• Falling unrolled toilet paper is very light for its surface area and probably has a terminal velocity of not much more than 1 m/s or 200 feet/minute, which should be easily beatable by a small aircraft even without particular acrobatics. Commented Nov 6, 2014 at 16:48
• I've actually had a parachute-plane pass me in free-fall when I was the last jumper out the door. :) Commented Nov 6, 2014 at 16:57
• "the descent speed of the airplane is not that much". The speed has nothing to do with that. What counts is the acceleration, because a free falling roll is accelerating at 1g, therefore the question is: Can an airplane accelerate more than gravity? The answer is it can, for a short time (maintaining a constant acceleration means reaching an infinite velocity). See this. "0-G" flights are done at 350 kt max, no big deal. Any bit more thrust and you are in the paper roll case.
– mins
Commented Mar 8, 2021 at 17:06

"I think the descent speed of the airplane is not that much"

I think you are wrong. Airplanes can descend very rapidly when needed.

The airplane is aerodynamic, meaning it slices through the air nicely, whether it is flying straight-and-level, or aiming straight for the ground. So its free-fall speed is much higher than that of a roll of paper, which will have considerable wind resistance.

In addition, the airplane has a propeller, which adds force. When in a dive, the airplane has gravity plus the force of the propeller taking down. But the roll of paper only has gravity.

I expect that in a full dive, the airplane could probably exceed a 10,000 FPM descent, or around 120MPH, which is around the terminal velocity of a skydiver.
(pulling out of a full dive safely is not easy, however).

The roll of paper will obviously and intuitively be slower than a skydiver.
I estimate it to be no more than 2,000 FPM, or about 20 MPH. (and probably a bit less)

(edit: In the comments, Henning Makholm suggests that a paper roll may only fall at 200 FPM. That is less than 3 MPH, which seems a bit slow to me. A slow descent rate for a Cessna when approaching an airport is 500 FPM.)

The airplane does not even need to enter a full dive to be faster than the paper. It could probably catch the paper with a nice, gentle 2,500 or 3,000 FPM descent.

• The speed depends on how much of the roll has become a streamer. I think your 2,000 fpm estimate is reasonable based on the linked video, maybe just a bit high. As it unrolls it will probably slow towards 200 fpm. Commented Nov 6, 2014 at 17:48
• Most planes can't descend at 10,000 ft/min because they would exceed their maximum design speed. Fast emergency descent in an airliner may be around 8,000 ft/min and that requires deployed spoilers. Commented Nov 6, 2014 at 18:44
• @abelenky: You need to stabilize the speed. Just diving will get you to 10.000 fpm, and the airplane will be intact to this point. But, lacking adequate drag devices, it will continue to accelerate and flutter soon after. Jan is right, too much descent will not be possible in a stationary way which includes a safe landing after having stopped the descent. Commented Nov 6, 2014 at 18:52
• I think the core point is that it is trivially easy for any plane to catch a roll of paper. Whether the max descent speed is 10,000 or 4,000, it is far faster than the falling speed of the roll. Commented Nov 6, 2014 at 19:06
• @ceejayoz If you chuck a typical GA piston single airplane into a vertical dive at 10,000 feet per minute (just shy of 100 knots) you could very easy to overstress the airframe and tear the wings off pulling out of the dive. (Presumably you've already got some forward speed when you enter the dive, so you'd hit 100 knots pretty quickly too!) That said, you don't need to go that fast to catch up with toilet paper: The MTO Sport Autogyro's max speed is only about 100 knots & it easily cut a streamer several times. Commented Nov 7, 2014 at 3:13