Slingshot Effect (QF32 p 346)

(Photo RDC)

Sunrise over the English Channel – Monday 22 September 2014.   Click to expand to very high resolution.  (Photo RDC.   Free use authorized if acknowledged)

Editor’s Note

I am pleased that this topic has generated much discussion in the pilot community.      Few readers understand if and why the Slingshot Effect exists which makes this topic is even more interesting.   

 

Question

(Photo RDC)

(Photo RDC)

QF32 reader John Reid asks:

“The QF32’s appendix includes A380 specifications.   There is a statement on page 346 for weight change variances due to “slingshot effect” between SYD/LAX/SYD…  What is the “slingshot effect”?

Warning – Technical Answer

Hi John,

Thanks for your question about the Slingshot Effect.

Ask any jet pilot who flies across the Atlantic and/or Pacific and they will tell you that the easterly flights generally burn less fuel than predicted and that the westerly flights generally use more.

This phenomena is real and can be explained by the “Slingshot Effect”.

Blue Marble (Photo NASA)

Blue Marble (Photo NASA)

The newest Global Positioning Satellites are launched to take advantage of the Slingshot Effect.   These GPS satellites are launched from vessels located about 3,300 miles southwest of Long Beach and 1,400 miles south of the Hawaiian Islands.  This equatorial site allows the rockets to use the Earth’s high rotation speed as better launching point to reach orbit faster and with less fuel burnt.

British Airways Concord at London Heathrow airport (Photo RDC)

British Airways Concord at London Heathrow airport (Photo RDC)

(Graph: NASA)

Variation of Saturn V payload with launch azimuth (Graph: NASA)

Other examples of the Slingshot Effect include:

The concorde was effectively 2.3% lighter than its curb weight when flying on an easterly track at the equator and 0.5% lighter when flying west. The designers relied on this significant effect when planning payload-range performance where the route performance margins were small.

Gunnery and ballistics experts anticipate that rounds (bullets) fired to the east always fly a little higher (drop less) than rounds fired (at the same angle and nil wind) to the west.

At Mach 4, the apparent gravity of a missile changes by a whopping 5.1% / 1.5%  for easterly/westerly directions respectively.

Spacecraft take off from weather-beaten Kennedy Space Centre in Florida (28° North) and ESA in French Guiana (5° North) to harness rather than fight the earth’s rotation speed.

The Saturn V launch vehicle was designed to take advantage of the Slingshot Effect. The lunar mission payloads were kept within 800 pounds of the maximum by limiting the launch azimuths between 72° to 108°.

Very Technical

(Graph RDC)

The Earth’s gravity as a function of latitude

Slingshot_Earth_Radius

The Earth’s radius as a function of the equatorial and polar radii and latitude

The Slingshot effect alters the effective gravity and the effective weight for a moving vehicle.

The Slingshot Effect is a function of the relative speed of the aircraft about the earth’s centre. Factors to consider when calculating the effect include: acft velocity (track & ground speed), latitude and cruising level. The Earth’s changing gravity is not an input as it can be derived from the latitude.

For terrestrial users, the saving in fuel burn is shown in QF32 (page 346) for an A380 flying between Australia and the USA.    Airbus and Boeing test pilots and flight engineers anticipate and account for the Slingshot Effect when proving aircraft performance (they fly east-west racetrack patterns and correct data for variations in the local gravity).  The published airline performance tables do not take account of the Slingshot Effect.

The Slingshot Effect is also called the Eötvös effect.  It is not the Coriolis Effect.

Airlines save fuel when accounting for the Slingshot Effect at the flight planning stage.   Below is my graph showing the Slingshot Effect for an aircraft at 500 knots groundspeed.  I have produced tables for other conditions of ground speed and altitude.  Integrate the effect over the flight’s changing altitude, track, latitude and ground speed to get the overall change.  Note the the slingshot effect is greater on easterly than westerly tracks.

SlingShot_500

Slingshot effect (Graph RDC)

Summary

The Slingshot effect is real and significant.   The change in apparent weight due to the influence of the Slingshot effect for an A380 flying Sydney to Los Angeles is shown at QF32 page 346.   For this route, the change in fuel used is about 33% of the change in apparent weight.

Airlines that account (in the flight plans) for the Slingshot effect save (fuel) money.   Not all flight planning systems infuse the Slingshot algorithm into their performance calculations, which is curious considering that fuel costs now comprise about 30% of airlines’ operating costs.

This post is only intended to be food for thought.

Calculations of the Slingshot Effect requires application of basic physics formulae.  Rather than spoon feeding readers with these principles, I’ll leave it to them to research mass, acceleration, gravity, oblate spheroids, weight and local weight.   The dopamine reward for success will make the effort worthwhile.  I’ll reveal more information about the Slingshot effect in my Big Jets book.

John’s response

Multiple sling shots overhead London Heathrow at 6 am 22 September 2014. (Photo RDC)

London Heathrow at 6 am 22 September 2014. (Photo RDC)

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