# Flight of a badminton shuttlecock

1. Jan 5, 2013

### ragsubra

I have been playing badminton for several years now. I noticed that players choose different rated speeds of shuttlecocks depending on local weather conditions. A few years back I made an analysis on the influence of effect of air temperature and humidity on the flight of a badminton shuttle cock. I deduced that there were significant difference in the distance traveled.

I invite readers to comment on the attached analysis. Would be great if you could share your personal experience when playing the game.

PS: I plan to do a similar analysis for tennis if I'm on the right track.

Cheers
Ragsubra

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2. Jan 5, 2013

### Staff: Mentor

• Which background do you expect for your readers? Some things are very basic - it should be obvious that gravity is pointing down, you don't have to mention it twice.
• Try to define parameters where you first mention them:
"A new parameter called the air resistance factor, q, is defined that
is easy to measure and is sufficient for analysis."
-> ok, a factor q is defined. Defined as what?
• You reduce the problem to the density of air, before you show that this density is the only relevant parameter. I would try to do it the other way round.
• I would stick to SI units everywhere - 30ft are about 10m
• I am surprised by the quick approach to the terminal velocity (<1% deviation after 10m), did you check that with your numerical calculations? My guess: The mentioned 30ft are 30m.
• "We have already seen how q can be measured fairly easily." -> how do you measure the velocity fairly easily?
• Concerning an analytic solution of (8): Give one (with reference to literature, if necessary), or do not mention it.
• (9) and following:
I think $\times$ is an ugly multiplication sign, $\cdot$ looks better. It is a pressure, so it needs units. T should be explained (temperature in K?). As T=35.85 leads to divergence, in which temperature range can you use the formula?
I don't think you use (5) to derive (13).
Gram=g, not gm
I don't see a final formula (or some sort of summary) for the final air density. You have to plug (14) into (11), (11) and (9) into (13) yourself?
• "3 different strokes – long serve, overhand clear, underhand
clear and short serve" - 3? 4? And how do those strokes look like? In 4.3, you replace "short serve" by "smash", and why do you list them twice?
• 4.1 could mention the initial turning phase of the shuttlecock, which increases air drag and partially cancels the discussed reduction.
• "At this point it would be useful for the reader to understand the dimensions of a badminton court." - just show them, without speculating whether the reader knows them or not.
• Everything in inch and feet now, why?
• 4.3.1 where does the difference single/double come from?
kph,kmph, whatever -> km/h
Shot angle -> relative to what?
Figure 5 should stop at the point of impact.
As there is no way to compare figure 4 and 5 (e.g. "where is t=0.8s in figure 4?"), you could mark a few corresponding points on both plots. This applies to all other strokes as well.
It reaches its slowest point after the highest point.
• 4.3 general: Try to use the same number of digits everywhere - not "50" and "50.0" (angles) and similar things in parallel. If the local conditions are always the same, you don't have to repeat them in all tables, just refer to them as "sea level" and "Bangalore" or something similar.
• Wikipedia is a bad reference, but you can try to use wikipedia's references.
• If language is relevant, look for a native speaker to fix several issues.

3. Jan 6, 2013

### ragsubra

I really appreciate your taking the time to read in detail. Quite an incisive analysis. I will work on the feedback.
I originally wrote this for a sports forum, but it turned out to be too technical there. In this forum, I guess it turned out less than full baked. I wish I had got it reviewed before posting.

4. Jan 6, 2013

### jim hardy

Golly i haven't played Badminton in decades. But i remember vividly how quickly the shuttlecock loses speed.
Even as a kid i realized there was something special about the feathers that affected drag. But i wasn't alert enough to notice changes with weather.

Thanks for posting your interesting paper.

I have to wonder though - and please take this as an honest question not a criticism:

A shuttlecock has so much area in its feathers that i'd think its drag is more skin drag (viscous) than form drag(pressure).
And - humidity must affect air's viscosity,

You might take a glance at this article for insight to viscous vs form drag
http://www.pilotfriend.com/training/flight_training/aero/drag.htm
it's "wetted area" that counts for skin drag, and that's why those old corrugated WW2 cargo airplanes were so slow.

and this one gives in paragraph 10 on page 4 a formula for viscosity of moist air
http://www.wiley.com/legacy/wileychi/morvayindustrial/supp/toolbox6.pdf
I'd figure how much viscosity changes over your humidity range before dismissing it.

old jim

5. Jan 7, 2013

### ragsubra

Thanks for the comment and pointers. I will investigate skin drag. I have a hunch this may be one of the reasons they were never able to make an artificial shuttlecock mimic the flight of the natural one under all conditions.
I need to do educate myself on these concepts first (I last studied fluid dynamics nearly 20 years ago in school). I may take some time on this, but I promise to do it :-)

6. Jan 7, 2013

### jim hardy

It was over forty years ago for me, hence my trepidation to say even a single word.

We learn a lot from humble things. I use an old fashioned metal flashlight to teach concepts of Kirchoff's current law and common mode voltage.

Your shuttlecock might be a very advanced aerodynamic gizmo - certainly a bird feather is.

old jim

7. Jan 11, 2013

### dgordon42

Atmospheric pressure not only depends on your altitude, it also depends on the weather. Where I live (Ireland) it changes from about 970 hPa (stormy winters day) to 1030 hPa (sunny summers day). This is equal to a change of altitude of about 2,000', all without leaving the ground!

Dave.

8. Jan 11, 2013

### ragsubra

Vow! That's some pressure change. Compared to that, I must really be in the doldrums. I think Bangalore has much stabler pressure. I happen to work in a project that uses a high precision pressure monitor. Over the last couple of months, I don't recall a change of more than 5 mm of Hg. I guess I'll wait for a cyclonic storm or the monsoons to see significant changes.

Thanks!