Ask A Scientist General Science Archive

name         Michael
status       student
grade        9-12
location     IL

Question -   What is the relation of the angle at which a Frisbee is
thrown to how far it will curve off in a horizontal direction?
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The aerodynamics of a Frisbee is not trivial, but only fairly recently has
it been given serious scientific/engineering attention. The trajectory
depends upon several factors and is too long for a question and 
nswer format like NEWTON
BBS. The best I can do is give you a fairly recent web site which gives a
lot more detail and relevant links:

http://mae.engr.ucdavis.edu/~biosport/frisbee/frisbee.html

Vince Calder
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Michael-
     I have definitely noticed this effect.  As a Frisbee duffer I 
 find it irritating.
I have thought about it a little, and have some vague ideas,
which need to be investigated mathematically or empirically before 
asserting them.

A Frisbee spins.  So it may have some gyroscopic precession effect.
This means that if the lift is forwards or aft of the disc's center-point,
the Frisbee will start tilting sideways ("roll" direction in 
aircraft parlance),
and then there will be a sideways component in it's normal lift,
which will deflect its path sideways.

Spinning also might create some differential drag (left vs. right) 
and/or lift.
Think about under that hooked lip: on the advancing side the surface 
is sliding into the wind,
and on the retreating side the apparent shear velocity is less.
If the Frisbee is spinning slow enough for gyroscopic effects _not_ 
to be dominant,
then differential lift could cause sideways tilt, again making the 
Frisbee veer horizontally.

Most classic tear-drop-shaped airfoils have their center of lift 
forwards of the
center of the chord, at about 1/3 of the way from front to back.
Suppose the instantaneous forwards half of the Frisbee is like the 
forwards half of a wing,
and the rear half is a rounded shape less optimal than the tapering 
rear half of a normal wing.
Then the Frisbee might be imagined as a center of lift at 1/3 from the front,
plus an additional center of drag somewhere in the rear half.
This drag has "Newtonian" lift  if the Frisbee is tilted fore/aft 
(pitch direction),
like any radically tilted plane plowing the air without good laminar 
flow (in "stall" condition).
Then if the Frisbee is level or slightly nose-down the drag would 
make an anti-lift in the rear.
Coupled with the lift in front and gyroscopic precession,
the Frisbee would be bound to tilt and veer quickly.

Conversely if the Frisbee was flying with a nose-up tilt, the drag 
would add positive lift in the rear.
This would balance out the forwards center of lift, and the Frisbee 
would not precess and not veer.
Just crude ideas of mine, probably not very correct.
I do not really remember whether tilting my disc nose-up or 
nose-down minimizes the veering effect.
You do your own experiments.

All this is equivalent to saying the Frisbee as an airfoil has one 
center of lift and one center of drag,
but they move around a little depending on the airfoil's angle of 
attack on the air.
Center of lift farther forwards would veer faster.
Center of lift shifted rearwards to the center of disc would veer not at all.
I do not know much yet about how these displacements are 
rationalized in most aerodynamic discussions.
You could probably pick up some ideas searching the web.

The spin-speed of your Frisbee-flip would matter.  Very slow would 
have weak gyro effects.
Medium would have strong effects.  Very fast would also be gyro-dominated,
but the effective angular inertia increases with spin speed,
so it might veer more slowly in response to a given off-center net lift.

A Frisbee hovering downwards slowly has an angle of attack greater 
than 45 degrees.
A normal airfoil would be well into stalled airflow condition.
But the Frisbee spinning may lubricate airflow differently than a normal wing,
maintaining gross airflow attachment,
so the overall flow is still something like laminar,
giving the Frisbee some lift even at ridiculous angles of attack.

At Google I typed [frisbee airfoil "center of lift"], and the only 
useful reference
found there was "http://www.microcfd.com/download/pdf/dissertation.pdf".
It numerically modeled an oblate ellipsoid because that would
compute in a more reasonable time than a true Frisbee-shape.
Page 118 has a pressure-map that gives an impression of an 
off-center distribution of lift.
Also it has a few references to studies and books on Frisbee aerodynamics.
Their results show centrifugal airflow (caused by the spin) 
lubricating the boundary layers.
The web site also offers airflow simulation software with a 3-day free trial.
Maybe If you find it worth buying and give it a few weeks on a 3GHz PC
it might show some results relevant to your question.

Googl'ing [frisbee aerodynamics] found more:
   - an instrumented Frisbee:
   
         http://www.lpl.arizona.edu/~rlorenz/frisbeenewscientist.pdf
		 
         http://probews2.arc.nasa.gov/abstracts/Frisbeeabstract.doc
		 
  - aerodynamics coefficients derived from videos of a throw:
 
http://mae.engr.ucdavis.edu/~biosport/frisbee/ISEA_2002_frisbee_0_151.pdf

  - thorough wind-tunnel tests:
  
        http://www.discwing.com/pdf/AIAA-2002-3150.pdf

These guys are just beginning to answer your particular question.
But It seems that the center of lift is always somewhere forwards of center,
so it always rolls and banks, only the quickness of the effect varies.
It also looks like faster throws have lift closer to center than slow throws.
It is acknowledged that faster spin slows the veering rate.
But it does not all quite feel complete yet.

Jim Swenson
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Michael,

The most accurate answer I can give is to say it is directly proportional.
(one increases with the other)

As the Frisbee moves through the air, its curved upper surface generates
lift.  This lift pulls the Frisbee straight up. (well, up relative to the
Frisbee anyhow, if you throw one upside down, expect it to dive to the
ground quickly!)  If it is tilted slightly to the right, most of this force
keeps the Frisbee from falling to the ground, but just a little of it will
pull it to the right.  Tilt it quite a bit to the right, and it gets quite a
bit of pull to the right.  However, it will get less pull up, and therefore
settle to the ground more quickly.

Ryan Belscamper
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