Aircraft traveling around the earth

Aircraft traveling around the earth

 

Question:

It is known that each aircraft has a fuel tank, which can fuel each other. The fuel in a whole tank can be used for a plane to fly around the Earth for half a lap. How many flights and flights are required for at least one plane to return to the airport around the Earth?

All planes take off from the same airport and must return to the airport safely. A plane cannot land in the middle of the airport. A plane takes off as a single flight, and the refueling time can be ignored.

 

 

CalculationAlgorithm(Johnny original ):

Set the fuel tank capacity of the aircraft to V, and the total travel route around the Earth to L. Initially, there were three aircraft A/B/C, the aircraft fuel consumption is 2 V/L (fuel volume/trip ).

 

Set the first three planes to fly together as S1. Then:

 

C. The oil that can be added to others (taking into account the returned results ):

 V-2 * S1 * 2 V/L

This value must be greater than 0, and the solution S1 <L/4 (that is, between 0 degrees and 90 degrees)

 

A/B total fuel consumption:

 S1 * 2 V/L * 2

 

When "C can be added to others" is equal to "A/B total fuel consumption", C's oil is used to the greatest extent. That is:

V-2 * S1 * 2 V/L = S1 * 2 V/L * 2

Solution:

S1 = L/8

That is to say, when S1 = L/8, C returns, and the amount of fuel consumed by the/B aircraft (respectively V/4) can be filled up.

 

[Now C has completed its mission, leaving a and B .]

 

Use the same method:

 

After the two planes go through L/8 respectively, if the two planes fly S2 together, then:

 

A fuel consumption:

S2 * 2 V/L

 

Remaining B oil (Considering Return ):

V-(L/8 + 2 * S2) * 2 V/L

The remaining B oil should be greater than 0, and S2 is obtained <7/16l

When "A consumes oil" is equal to "B remaining oil", B returns, and B's oil is used to the greatest extent. That is

S2 * 2 V/L = V-(L/8 + 2 * S2) * 2 V/L

Resolution

S2 = L/8

(Equivalent to B's return after a joint flight of 45 degrees and hand over all the remaining oil to A, A's oil is full ).

 

In this way, when a has gone 45 degrees and 45 degrees, it can still go 180 degrees, 90 degrees away from the target.

In the same way, plane A can fly around the world.

 

Three planes and five flights are used in total.