Here's an interesting, yet worthless discussion.

Two airplanes identical in geometry are flying at the same altitude above ground. One of the airplanes weighs twice the other. The airplanes are going to race to the ground to see who can come down faster. The hitch is both airplanes have the same maximum speed, meaning they will flutter apart if flown faster than that.

So, which airplane reaches the ground first and why?

the lighter one ?!

I believe (guess) the heavier one would accelerate to it's terminal velocity faster than the lighter one because the extra weight is always accelerating the aircraft toward the ground even in level flight, so it would reach the ground faster. Sort of like two cars raceing to a red light in a 60 MPH zone. Neither goes over 60, but the one that reaches terminal velocity the soonest gets to the red light first. If they were going straight up, the lighter one would win. I can only imagine the soon-to-come dozen pages of amusing yet ill-informed jargon. Not that I am any different
-Steve

The lighter one! Acceleration due to gravity is a constant, but the lighter plane will have greater acceleration due to engine thrust

Interesting proposition, and we must, of course, make a few assumptions, to wit: A: I will assume that they are flying high enough so that the airframe failure airspeed, which is the same for both airframes, will be approached by both aircraft for 90% or so of the duration of the decent, B: I will assume that the airframe failure airspeed can be exceeded (disasterously) by either aircraft through a combination of power and gravity exceeding the airframe drag at that airspeed.

With only these assumptions, both planes could get to the ground at the same time, but if we assume that the heavier one is prone to exceeding the failure airspeed in a vertical dive with minimum thrust and maximum drag, (and must therefore shallow out the decent angle to keep the airspeed below failure velocity) then the lighter one will be able to safely get there first by diving at the same airspeed and a steeper angle.

The heavier one descends at the higher rate.

Vector resolutiion of balance of forces illustrates.

WEIGHT vector of one is twice that of t'other whilst THRUST if a speed limited constant, DRAG and LIFT vectors remain equal. Assuming both aircraft emerg. descend at constant equal max. speed (Vne structural limitation) with power (being proportional to thrust) adjusted to maintain constant speed and therefore proportionally constant thrust, and with it lift and drag resolutions identical for both. However, weight of one is twice that of the other resulting in double the weight vector (always acting perpendicular to the surface of the earth) and consequentlally a higher descent rate.

The heavier plane reaches it's Vne at a glide slope that is less steep than the light plane so the verticle component of the light plane's velocity will be higher. If the plane is light enough and draggy enough, it may be able to dive vertically without exeeding Vne.

Full scale gliders don't carry water ballast for nothing.

But what is the VNE speed? Is it more or less than terminal velocity?
Is the race power on or power off.
IF the heavier one breaks up and the wings "flutter" to the ground they will reach the ground after the lighter plane, however the lawn dart fuse will impact prior to the lighter plane.

The Vne speed is less than terminal velocity.

Vne is the Not Exceed velocity. In this hypothetical case you can take it to mean the speed just before airframe failure. So it is the same for both planes.

A lot depends on the flight path that the models can use. If the prop at idle provides the braking force needed to avoid Vne for the heavier model then both can follow the same descent path. If it doesn't then the glide slope and vertical velocity components comes into play.

If they can both dive vertically then the one that is ahead at the time the second one reaches Vne is the winner. For my money that would be the heavier one since if they both start from level flight the heavier one is going to have more "power" in the form of the engine thrust added to by gravity to reach it's Vne sooner than the light one. Remember that air drag is present in level flight and during the diving acceleration. THe heavier one will be in a better position to accelerate to Vne faster despite the drag than the lighter one. In effect the extra weight provides more thrust than the lighter model. The bit about objects accelerating at the same rate when dropped only applies if there is no air drag. A feather and a copy of the feather made from lead will both accelerate from a standstill at the same rate but the lead feather reaches a far higher terminal velocity.

I'm assuming that they will land, rather than dive straight into the ground. I'm going to ignore the bulk of the descent & call them equal until the landing pattern. I'm also going to assume that they are landing on a straight-in approach.

The heavier aircraft will win.

Its rate of descent in approach & its approach speed will be higher, It will actually touch down on the runway first.

"The heavier..."
That's why soapbox racers have a weight limit!
Heavy makes fast!

Yes, but soap box racers don't have a Vne.

To make it clearer, assume that the starting altitude is so high that both planes reach Vne well before they reach the ground, in which case the bulk of the descent is the important part.

That changes things. The lighter aircraft will have a steeper angle of decent, & at the same airspeed as the heavier aircraft, it will reach close proximity to the ground more quickly --- whereupon the heavier aircraft will begin to catch up during the landing approach -- hmmmm.

Noting that the bulk of the descent is key, the lighter aircraft will win -- unless they are both many miles away from the airfield, whereupon the heavier aircraft will win for previously noted reasons.

Descent rate, ie: "which reaches the ground first" is a factor of time, not angle. It's true, gliders don't carry water ballast for nothing, but for reasons you apparently don't understand at all.

eg: Assuming two gliders (eg: Discus b) with the same L/D (hypothetical nil W/V) one (full tanks) and the other none are both flown at respective speeds for best L/D. Does one reach the ground first? The answer to that is yes. See if you can explain which and why. Assume both are flown at Vmin sink. Does one still reach the ground first? Answer and why?

Quite apart from the absurdity of your suggestion of a light plane (ie: general case, not being eg: WWII mil dive bomber with speed brakes extended) being able to dive vertically without exceeding Vne, no parameters were given suggesting the case of a light plane or otherwise, which incidentally is immaterial. Certain assumptions must be made. Assuming you were trying to descend at as high a rate as possible, the limiting factor before the nose got too pointy toward ground would be speed and the limiting speed (structural) a professional pilot would fly at would be Vne.

Edit: sp

Vne is the industry abbrev. for Velocity Never Exceed and is a structural (vs performance) limitation. It is the maximum target speed (IAS) at which the plilot would deliberately fly without risk of structural deformation or failure. It is factored marginally below that at which the airframe will actually fail. It is less than "terminal velocity".

Unstated in the question, but for those with an educated and experienced inkling, type dependent it'd be reduced power or flight idle differing in both aircraft to maintain constant IAS of Vne.

I'd sugggest the term "plane" implies all parts still in expected formation and as any pilot knows, at Vne, otherwise the word wreckage would have been more appropriate.

Hi Bruce

Well thought out answer. But, there's always one isn't there, the limiting factor regardless of type from glider, through light aeroplane, turboprop or passenger jet will always be Vne. Basically if you hypothetically wanted to get down fastest (rate) you possibly can, called an emergency descent and an IA followed in the case typically of explosive decompression, fire (unextinguished) or oxygen malfunction (assuming very high) you point the nose at the planet. The limitation as to how far you can point the nose will always be Vne. Given that at Vne, a constant speed, no matter the source, the thrust vector must be the same for both aircraft. Therefore at a constant speed, the drag vector is also equal. leaving us lift and weight to resolve. Now lift must be equal for both given already stated aerodynamic equality and that L=cL½RhoV²S with the only effective variable airspeed, and as already stated we are descending at the same max (controlled assumed) which will mean at Vne. The remaining vector, weight, a force (mass x acceleration) which is acting perpendicular to the earth vectorially is disproportionaly higher mathematically for the heavier aircraft. Therefore it will descend at a the higher rate of descent and reach the ground first.

We aren't discussing two objects in gravitational freefall, but power settings or initial acceleration in descent are obfuscational 'considerations' intended to confuse. The limiting factor in this case will be a structural rather than performance limitation, and in the general case given, we have to make some assumptions from the implied general in the absence of supplied specific. That presumption would be that the aircraft would be flown at Vne in such an emergency which would avail max. rate.

To revisit it in a simpler illustrative case to demonstrate gravity works, take two identical gliders. eg: Duo Discus. One is two up the other solo. The dual occupied unit is also carrying full ballast (water). Both flown (still air, nill wind) at their respective Vmin sink (min ROD), the heavier glider would reach the ground first. Fly them both at respective best L/Ds. Range would be identical, but the heavier glider flown faster would still reach the ground (and destination) first. Even if you had them descend at their Vne, the heavier glider would still reach the ground sooner due to resolution of the balance of forces. More lift is required to counter the increased weight. That increased lift is ordinarily obtained though flying faster. If both are flying at the same speed (Vne) such that their lift is equal, and one is heavier meaning the weight vector pointy toward planet is larger, it's pictorially apparent which one is going to descend at the higher rate and reach the ground first.

Edit sp & clarification

you don't need to know anything about "aeronautics"
two craft same weight
same power ????????
without that factor beingincluded -- the question is just a que-----
but the one with best acceleration will win-
any drag racers out there ?
We once raced a gas class - based on cu in to weight - we won -consistantly
we had the fastest acceleration- usually not the fastest top speed
In my view of this conundrum--when the flag dropped -- the planes both jammed in to a full power vertical dive
the one with the lowest elapsed time to VNE - won.
It's a vertical drag race.

Except what happens at VNE? It ain't all over at that point unless both aircraft have dive brakes that can limit the speed to VNE. If that is not the case, then both aircraft will have to pull up to limit airspeed to VNE. One or other will have a steeper angle of descent. As noted by the initiator of this quest, the bulk descent predominates -- The aircraft with the steeper angle of descent will win. Which one Sherlock?

So what next sherlock?

You integrate S=1/2a*t^2 for each plane, to Vne.
One plane will reach Vne before the other. At Vne the descent speed is the same, so the "winner" is the one that hits the ground because it went further during the acceleration phase.

TO answer this correctly we need to know the specifics of when the aircraft reach Vne. As I said in my earlier post, if the prop and airframe drag is capable of holding both airplanes to Vne in a vertical dive that's different than if they need to assume a steep gliding dive to hold the speed back. If vertical the heavy one wins as it reaches Vne earlier in the dive and since they both fly down at the same rate from that point on then the lighter one can never catch up.

If the dive/glide angle forces the planes to Vne before a vertical attitude for both planes is reached then the lighter one gets down first as the vertical component of it's speed is a greater portion of the Vne speed.

So to settle this we need to define the test conditions more clearly.

Sigrun, there is a problem with your assumption that both airplanes have the same L/D. Assuming both are operating at the same speed (Vne) then the one with the higher wing loading has a higher L/D.. You discounted BLE's post, but BLE is the only one that hit it right on the head. The principle behind this question is the inverse of the principle that drives glider pilots to add ballast. Increasing wing loading allows you to increase your cruise speed while keeping the same L/D, which results in the same glide ratio. Or conversely, it increases L/D if the speed is kept constant. That is why wing loading is one of the most important design parameters for high performance aircraft.

The converse of this is that for the heavier airplane to have the same speed as the lighter one, it has to have a lower descent rate because the drag of the two is essentially equivalent. (There is a difference in induced drag due to the fact that one aircraft is operating at twice the lift coefficient of the other, but this is small.) The best way to think of this is to have two cargo trucks with the same braking capability but different weight. The lighter one can go down steeper grades without overspeeding.

Sig, you are overlooking the lift coefficient in the lift equation. If two airplanes with the same geometry but different weights are flown at the same speed, then they are flying at different angles of attack meaning different lift coefficients. If the lift force was the same for the two aircraft then the heavier one would be accelerating downward meaning it's speed would increase. Also, you stated that it is a matter of time not angle. Well, look at it this way. If the magnitude of velocity is the same, but the angle of descent is larger for the lighter aircraft, then the descent rate magnitude is also larger.

I don't mean to give the answer away, but I think the discussion will still be just as animated if not more.

Dick, reread the question. Two aircraft, different weights. And try to use something resembling a normal sentence structure. No offense intended, it's just hard to read.

Also, a lot of people (even scientists and engineers) think that something with higher mass will accelerate towards the ground faster. Errrr, wrong. If two objects have the same mass, and geometry (i.e. same drag) they will ACCELERATE towards the ground at exactly the same rate. The heavier one will have a higher terminal velocity, but that doesn't matter for this question because the Vne is below the terminal velocity.

oh dear - -this is like the conveyer belt thing -
there was nothing real about the question -it was a "whut if" thing
when you hit VME- you stick your hands out and hold back speed . No one said how large the planes were or how large your hands could be .
again - the question is incomplete - so given the info provided - the only answer is - one which gets to VNE the quickest------- wins
I did read the question -a few times
the weight is given -
but where does it say the race is based on just the weight?
the lightest one will accelerate the fastest - if power is identical--
but where does it say "chop power point nose down"---
You read the question as "which falls the fastest"- yes?
The structure of the sentences which used by me are hard reading?
that is a situation up with which one should not put!

Not so Britbat.

Angle of descent is a gradient and has nothing to do with rate which is the function of vertical distance/time. It's easier to see if you look at the reverse or climb example.

RoC and AoC are two totally different (ordinarily) performance (limited) criteria, with the latter not involving a time parameter, rather height gained vs distance travelled aka angle or gradient. If you were to examine both from the perspective of which one achieves best time to altitude, have a guess why best rate of climb (ordinarily spec'd as an IAS or MACH #) is termed best "rate"? If the two were the same there'd be no need for distinctively different speeds, and if best AoC also offered best rate, then we'd fly it wouldn't we? The same holds true for descent, only the direction and influence (assistance) of gravity is different. But instead of the limitation during descent being a performance limitation (excess power available), it is ordinarily a structural one. eg: Vne or how fast can we legally and safely go before the structure risks failure. As an aside, best AoC is ordinarily lower than best RoC and similarly for descent max AoD is achieved at a lower IAS than max RoD. Abundantly evident when illustrated by plots on respective performance curves. There's a big RED line and audio cues annunciating Vne for a reason. [8D]

Your statement above is misleading.

If by "descent speed" you presumably (context) mean to imply descent rates (descent as a function of time) are identical rather than descent speed (ie: Vne an IAS or target MACH), then that's a false premise. Of course if both are flown at Vne, descent speeds ipso facto must be identical.

Edit: clarification