Helicopter inside a trailer problem

[T. R. Oglodyte Moderator Find all posts View Profile Close T. R. Oglodyte]

Consider a helicopter parked inside a trailer. The trailer is parked on a truck scale. The bottom of the trailer is 20 times the size of a typical heliport, i.e., big enough for a helicopter to maneuver to take off. The sides of the trailer are 400 feet high - high enough for a helicopter to hover. The top, bottom, and sides of the trailer are air-tight. The trailer, when empty, weighs 10 tons, the helicopter weighs 3 tons, and the helicopter carries 500 lbs of fuel, and fuel will last for one hour. (I know, the helicopter is a fuel guzzler.) The trailer also contains a 1-ton weight, resting on the floor of the trailer next to the helicopter. (The 1-ton weight is not included in the 10 tons trailer weight.)

A pilot starts the helicopter and raises the helicopter to a hovering position inside the trailer.

Questions: What happens to the weight of the trailer when the helicopter takes off and hovers inside the trailer? What do you think the trailer weighs before the pilot starts the helicopter and immediately after the pilot takes off in the helicopter? What happens to the weight of the trailer as the helicopter is hovering? If the helicopter, as it hovers, lowers a cable that hooks on to the 1-ton weight and then raises the weight off the floor of the trailer, how much would the weight of the trailer change? If the pilot sets the weight down and continues to hover until the fuel is consumed, how much does the trailer weigh just before the helicopter runs out of fuel?

For purposes of this problem, assume that air circulates adequately inside the trailer so that the helicopter is stable when hovering. Also assume there is ample oxygen inside the trailer to combust the fuel, and that there is no heat transfer across the walls of the trailer.

Don't forget to consider that as the helicopter combusts the fuel, the fuel converts from liquid to gas, adding to the air pressure inside the trailer. Also the combustion of the fuel will increase the temperature inside the trailer.

[Oracle Senior Member Find all posts View Profile Close Oracle]

The weight does not change. In order for the helicopter to fly, it has to push down on the air with enough force to displace its weight. This causes the air to be forced down toward the bottom of the trailer. When the air hits the bottom of the trailer, it imparts the same force as if the helicopter were sitting on the bottom of the trailer.

Zero sum.

[T. R. Oglodyte Moderator Find all posts View Profile Close T. R. Oglodyte]

The weight does not change. In order for the helicopter to fly, it has to push down on the air with enough force to displace its weight. This causes the air to be forced down toward the bottom of the trailer. When the air hits the bottom of the trailer, it imparts the same force as if the helicopter were sitting on the bottom of the trailer.

Zero sum.

So what happens as the fuel is combusted and the weight of the helicopter decreases as it hovers?

[Spence Super Moderator Find all posts View Profile Close Spence]

So what happens as the fuel is combusted and the weight of the helicopter decreases as it hovers?

Conservation of Mass inside sealed container?

[bigfrank Administrator Find all posts View Profile Close bigfrank]

I would need 3 pots of Coffee before even attempting to answer this one.

[Oracle Senior Member Find all posts View Profile Close Oracle]

The products of combustion are added to the total weight of the enclosed atmosphere. It goes from resting in the tank as fuel to being combined with the oxygen in the trailer to form CO2, H2O and various NOx compounds.

The pressure inside the trailer will increase due to two factors: The expansion of the fuel though the combustion process and the expansion of the volume of the gas as the temperature rises under the perfect gas law.

Same thing happens when you fill a basketball with air. The weight of the ball increases as it is filled with air.

In this case the fuel just changes state, but is not removed from the system.

Again, Zero sum.

[Kay H Senior Member Find all posts View Profile Close Kay H]

Sounds like engineers corner .

[bnoble Senior Member Find all posts View Profile Close bnoble]

Nothing in. Nothing out. Nothing changes.

(IIRC this is also the subject of a recent/soon-to-air Mythbusters...haven't seen it yet though.)

[tonyg Goomba & Super Moderator Find all posts View Profile Close tonyg]

Can't get to it now, still working on a voilin question.

[bnoble Senior Member Find all posts View Profile Close bnoble]

As an aside: In the ideal frictionless spherical world of college physics, I don't think heat transfer matters (much) and the pressure change is a red herring. PV=nRT, so as T rises, P rises. But, n is not affected by the temperature/pressure change. n is affected by the production of exhuast gasses (CO2 and water vapor), but the mass of those gasses is equal to the mass of the combusted oxygen/fuel.

If heat transfer is allowed, then T decreases, so P decreases, but n remains constant, so there is still the same mass in the truck and it still weighs the same. In straight combustion, the heat is not a by-product of converted mass. Rather, it is the by-product of moving electrons in the fuel/oxygen from a state of higher total energy to the lower total energy state of CO2/H2O. Allowing that energy to escape the truck still doesn't change the mass in the truck.

Now, if the helicopter operates via cold fusion, well, then the energy is coming from mass conversion, and there you've got some more complicated reasoning. But, my intro quantum grades weren't nearly as good as those in classical physics...

[T. R. Oglodyte Moderator Find all posts View Profile Close T. R. Oglodyte]

Now, if the helicopter operates via cold fusion, well, then the energy is coming from mass conversion, and there you've got some more complicated reasoning. But, my intro quantum grades weren't nearly as good as those in classical physics...

Actually, the heat of combustion within the molecules of fuel is stored as mass, and that mass is converted to energy when the fuel is combusted. One of my school chemistry teachers had us calculate the decrease in mass that occurs in a mole of benzene when combusted, using E=Mc^2 and the heat of combustion for benzene. The change in weight is so infinitesimal - IIRC, it was somewhere around 0.00000001% - that for all practical purposes and virtually all theoretical purposes the change in mass associated with non-nuclear reactions can be ignored.

[bigfrank Administrator Find all posts View Profile Close bigfrank]

I bet if I ate beans and flew the helicopter , I could add to the gas.

[T. R. Oglodyte Moderator Find all posts View Profile Close T. R. Oglodyte]

Interesting replies.

The answer is quite simple. I give Spence the award for best answer - it's a closed system, so the mass is unchanged.

It's not necessary to even consider the downward air pressure exerted by the helicopter blades. All you need to know is that the trailer is air tight.

All of the other details are just red herrings.

***

Now for a related question that might be trickier.

While the helicopter is hovering inside the trailer, the trailer is connected to a truck and the truck begins to haul the trailer in a straight line at a constant speed - say 60 miles per hour.

Does the helicopter move right along with the trailer, or will the pilot need to make adjustments to keep the helicopter stationary and free from rotation as the trailer starts to move?

[RESORT2ME Senior Member Find all posts View Profile Close RESORT2ME]

Steve,

"Do or do not... there is no doo-doo."
---------------------------------------------

Your signature says something close to my thoughts. haha

I've flown many a helo but never in an enclosure.

My imagination tells me, the flight suits would never be worn again.

[bnoble Senior Member Find all posts View Profile Close bnoble]

I believe the pilot needs to adjust. If it were a vacuum, the copter would go "backwards" in the truck just as fast as the truck goes "forwards" thanks to Newton's 1st. However, the truck has an atmosphere. So, this is equivalent to a 60 MPH tail wind (assuming the helicopter faces forward) relative to the "outside". (Edited to add: it also assumes the atmosphere is completely stiff, which is patently untrue.) But, a 60 MPH tail wind doesn't push the aircraft forward at 60MPH. So, I think you still need to adjust, just not as much as you might in a vacuum.

Also, I dug up this very interesting lecture on the equivalence of mass/energy. My understanding of combustion does appear to be strictly classical, and the relativists have refined the idea. Cool.

Mass and Energy