Physics for the Coffee Table – Quiz # 7 – Seven Winners!

Situation

My son Alexander in the A380's cockpit at Dubai Airport (November 2013)

My son Alexander in the A380′s cockpit at Dubai Airport (November 2013)

I had the privilege last week to address a large audience at the Royal Aeronautical Society at the Engineering School at Cambridge University in the UK.   (click here for more information).

The next morning Dr Hugh Hunt (Department of Engineering) showed my son Alexander and I around the Trinity College and the Trinity Clock Tower.

We returned to Hugh’s office after the tour where we played with his bi-metallic clock pendulum, tuning cylinders, tuning forks and other remarkable (engineering)  toys.

Trinity Clock (Photo Alexander de Crespigny)

Trinity College Clock (Photo Alexander de Crespigny)

I thought of this week’s question whilst throwing Hugh’s boomerang around his busy office (and trying not to injure his students).

Welcome to Trinity College, Cambridge

Photo: Trinity College, Cambridge (www.trin.cam.ac.uk)

Question 7

a.  Why does a boomerang return to the thrower?

Lifting and pitching forces cause the boomerang to fly in an orbit path back to the thrower.

The boomerang is similar to a helicopter.

Imagine the paths of the rotating blades tracing-forming a rotating disk.

The rotating blades (wings) generate lift.   The blades passing perpendicular to the flight path (front and rear) generate the same lift.   The advancing blade generates more lift than the retreating blade.

Thus the net forces on the disk are:

  • lift (to keep the boomerang airborne); and
  • an additional “rolling” force (moment) that is positive/negative for the advancing/retreating blades respectively.

The “rolling” force causes the spinning boomerang “disk” to precess like a gyroscope or bicycle wheel. The disk displaces in the axis that is rotated 90 degrees forward from where the force is applied.

For the boomerang, the precession  force provides the result similar to a canard or elevator on an aircraft, pitching the boomerang’s nose up.

The constant bank angle and pitching causes the boomerang to “orbit”.

b.  What is the maximum and minimum number of airfoils (wings) on a boomerang?

Just the same as a helicopter:

  • Maximum blade count – unlimited
  • Minimum blade count – one.   Modern hunting boomerangs have one blade with a counterweight on the other side.

Summary

It’s easy to work out how to throw a boomerang when you appreciate that the “rotor disk” needs a high rotational rate to generate lift, and then a high forward speed, to generate the precession forces that powers the pitching effects.

Happy throwing!

  • Flares of venting gas soften the Iraqi sunrise.   28Nov2013 (Photo Richard de Crespigny)
    Flares of venting gas soften the Iraqi sunrise. 28Nov2013 (Photo Richard de Crespigny)

    Quiz Prize

    The first person to answer both questions correctly may chose their prize from the selection of Category 1 prizes.

    The winner will be announced on Thursday 5th December at:

    • 7 am –  New York
    • 4 am – Los Angeles
    • noon – London
    • 1 pm – Paris
    • 8 pm – Singapore
    • 11 pm – Sydney

Winners

Again, unfortunately, there were no people who correctly answered both questions.

However, I appreciate the effort you all took to tackle this question in the true spirit that I intended when I wrote “Physics For the Coffee Table”.

We are also approaching the Christmas break at the end of another challenging year.

So to kick start the festive season, I therefore deem all seven people who submitted answers to be “close enough” to get a prize.   I’ll be in touch…

Thanks for joining in the fun, and Merry Christmas!

Thanks

The QF32 Web Site Crew thanks Pan Macmillan and Airbus for providing these excellent prizes.

See also

Physics for the Coffee Table

7 comments

  1. a) Bernoille: On a upper part of a wing the airflow is faster than under the wing, so the pressure on the upper part is lower, which forces the wing to go up.
    The boomerang is thrown in a vertical way, rotating, so we have an addition of two directions: The direction in which the boomerang was thrown and the direction resulting from the wing-construction. This results in a circle so the boomerang is coming back.
    b) Minimum 2 wings
    The Maximum should be limited by the distance between the wings, so the air-turbulation behind the wing can occure. ( I have seen boomerang with 4 wings)

  2. a. Assuming we have a right-handed boomerang, looking at it as an inverted V from the top the airfoil is on the right so the boomerang will always turn towards the left and, if thrown at the correct angle to the wind, will return to the thrower.
    b. Only one side of a boomerang is angled to act as the airfoil so the answer is one for both maximum and minimum.

  3. The boomerang “flies” because it has wings that act as foils and they generate lift.

    It “returns” because one of the foils generates more lift than the other (the one on the top when it is advancing in the same direction of the movement and because of the gyroscopic principle (force acts 90 degrees with respect to were it was applied)

    The combination of all of the above allows the boomerang to stay in flight longer than a piece of wood and to turn in one direction instead of flipping over.

    As to how many blades: If it is a returning one it seems that up to four.

  4. a) The reason the boomerang comes back is because of the difference in air flow over the two wings.

    I imagine the boomerang spins around an “imaginary” axis where the two wings meet (in the middle). This spin, with the speed initiated by the thrower and the design of the wings as airfoils, will cause the boomerang to move in a circular curve as the wing “on top” will have greater lift to one side, due to the fact that air flow faster over one of the sides.

    b) two wings will be necessary for it to return and they have to create a “corner” meaning an angle less than 180 degrees. There could be more wings on it but my guess is that there should be a certain distance between the wings so that the effect of a circular curve is achieved by this difference in air flow over the wings. Some limits with construction etc is also a factor for how many wings you can have on one (returning) boomerang.

    Sorry for any spelling :) it would have been nice to be able to draw.
    /Johanna

  5. Shaun Amy · · Reply

    7(a)

    You throw a boomerang near to vertical. Each of the two “arms” are shaped like a wing (airfoil). The leading edge is at the top of the boomerang so as it goes through the air you get lift and it “flies”.

    However, this “lift” creates a torque induced or gyroscopic precession which can be most easily described as a change in direction of the rotation axis. The classic physics example is the child’s spinning toy top.

    So for a boomerang, there is an angular velocity component at right-angles to the direction the boomerang is travelling causing it to trace a circular path that bring it back towards the person who threw it.

    7(b)

    Minimum is two, one on each arm of the boomerang and maximum is three (if you include the airfoil at the centre of the two arms). To be honest I am rather unsure of my answer to this part.

  6. Rachel Stevens · · Reply

    The aerodynamics of the wings (or foils) of a boomerang behave just like those of an aircraft, whereby a difference in air pressure above and below the foil is created which keeps the boomerang in flight.

    Returning boomerangs return to sender when thrown correctly – at the right speed, with sufficient spin.

    They must also be launched vertically (rather than horizontally)! Why is this ? Because the foils face in opposite directions each wing is travelling forwards as the boomerang spins; this generates “lift”, keeping the boomerang in flight. Bearing in mind the boomerang is thrown vertically the top wing travels at a faster speed than the lower wing. This force imbalance causes the boomerang to rotate around its vertical axis (a bit like a spinning top) and acts as a centripetal force, making the boomerang follow a curved course and allowing it to return to the sender.

    The minimum number of foils is two ; in theory there is no maximum (provided the foils do not become so densely concentrated as to form a solid disc surface).

  7. a. The torque as a result of differences in lift between the various airfoils
    b. minimum 2. max unlimited, in practice 4.

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