I am not sure if this would work but if it did work it would be of some value. In archery flight shooting our goal is to build an arrow with the minimum drag. I have always wanted a way to measure this objectively. so I was wondering if what I am going to describe might work. One test we use is to attach a very fine string to a point near the center of the arrow., attach that string to a stick and then spin the arrow in circles watching it’s flight. It is useful but says nothing of drag. If I could use a small motor to spin the arrow instead of human power would simply taking an amp reading of the motor at a specific rpm give me info on the drag?
Your proposed test is probably not as accurate as wind tunnel testing.
Aerodynamic properties of an archery arrow:
That would definitely be a superior method. It might be too hi tec for the garage. It will take me a while to digest that article. Typically, we will be out on the garage building and designing arrows. It would be nice if there were a low tec inexpensive way to test them.
As you point out, spinning the arrow on the end of a string doesn’t actually tell you anything about the drag on the arrow. It doesn’t even tell you the difference in drag unless you control all other elements of flight.
If I was trying to judge which arrow would cut most smoothly through the air (so let’s call this overall aerodynamic drag), I’d try to set up an impact sensor to measure the impact force of an arrow fired a fixed distance by a reproducible initial force (so a mechanical bow setup or a pressurized launch tube).
Measuring the impact force and the exact mass of the arrow being tested (by weighing it), one could calculate the velocity of each arrow fired and if one ascribes the difference in velocity to “drag”, you can tell which arrow has the highest velocity/lowest “drag”.
When the arrow is shot from a bow you are introducing another factor. Archers paradox, this si where the arrow flexes as it leaves the bow. This is actually one of our biggest problems to solve. Getting the arrow out of the bow cleanly. A lot of speed is lost during the first few feet of flight until the arrow straitens out. The arrows are extremely light compared to a target arrow, around 180 grains. This problem is usually solved by tuning the arrow to the bow and having proper spine on the arrow. But it would affect the other measurement so they would have to be isolated from one another.
That’s why I put quotes around “drag”, because it doesn’t measure true drag, just which arrow is more aerodynamic. Of course, one needs to have an identical launch for each trial, which is why some mechanical setup (including using a tube launch) is best.
This paper shows that two methods, wind tunnel (best) and use of high rate cameras (more affordable) can be used to calculate drag. They also use a launcher and an expert archer in their experiments.
Free Flight and Wind Tunnel Measurements of the Drag Exerted on an Archery Arrow
From the paper:
In this paper, we conduct two support-interference-free measurements of the aerodynamic forces exerted on an archery arrow…
…We also perform a flight experiment, in which the drag coefficient is determined from the velocity decay rate. The arrow-shooting system using compressed air as a power source, developed in [3] was used.
Also:
The oscillation of the arrow launched from a recurve bow always makes the boundary layer turbulent, which assures the high repeatability of shots by an expert archer.
You don’t happen to have access to a couple of high rate cameras?
No, I wish I did
Well, they use a 2000 fps camera in the experiments described above, but you could get away with lower fps at the cost of precision in your results. Amazon has what claims to be a 1000 fps camera listed for ~$170.
Casio Exilim EX-FH20 9.1MP Digital Camera 20x Optical Zoom 1000 FPS
As an experimentalist, I can say that it is usually going to be the cost of measurement that is going to limit what you can extract, not the cost of “flying” the arrow. You can probably duplicate the paper’s launcher for less than $50, but will need (relatively) expensive instruments to measure any property worth measuring with any accuracy.
Most research universities with aerospace engineering departments have wind tunnels. If you could get a professor interested, then you could do wind tunnel experiments for free (though you would still probably have to do the data reduction).
Of course, with the knowledge that your accuracy would be much less, there are instructions on how to build a DIY wind tunnel out there…
Build Your Own Wind Tunnel (NASA)
Here is a wind tunnel design that was developed at NASA Glenn during the Centennial of Flight Celebration in 2003. This tunnel can be built for less than $100 and uses a computer fan motor to move air past small models. Complete plans for the tunnel can be downloaded for free from the web page.
With that, I’m out. But I’ll leave you with some unsolicited advice.
I have no background in aerospace engineering (though I work with some aerospace engineers). All of my posts are the result of a total about 15-20 minutes of thinking and googling. My posts took longer to write than to research.
Before proposing experiments like the one in the OP, you should spend at least a few minutes researching: 1) Are there already ways of accomplishing what I’m trying to accomplish?, 2) What would my set up produce that is measurable and how would I measure it to the accuracy I might need?, and 3) Would my approach (including measurement and data analysis) be better in some way (better can include cost and convenience) than existing methods?
Accelerometers have made some advancements and have never been smaller.
I have actually been involved with this for the past 25 years, the last 10 years only sporadically. There are quite a few engineers enjoying this hobby and no one has really came up with anything yet that produces any worthwhile data. The differences in drag would be extremely small and difficult to measure I imagine. Stability is a huge factor as well. Flight arrows are finicky, light and at best inconsistent. I would feel pretty good just making a little progress on the shape of the arrow. So far the Turks have come up with the best designs several hundred years ago. We still use that design today but always looking for incremental improvements. Not dealing with very high speeds, these are primitive bows and speeds would be well below 300 fps.
Three thoughts.
Drop the arrow into a column of liquid (air substitute) and measure time to the bottom of the column. Or drop the subject arrows from a suitable height as in a building or warehouse and measure time to impact. You may not generate enough speed to produce the difference level you’re looking for.
There are golf ball/swing equipment that measure ball speed using doppler radar. A machine can simply measure the initial velocity or two machines at set distances with an arrow passing through their view window would give you a speed variation. The machines range from a few hundred to $7000.00 plus. Many golf/sport shops have them. Perhaps you could interest them in an after hours experiment. The accuracy of the cheaper machines may be too little.
A search for “measuring bullet velocity” will get you equipment and youtube videos on how bullet velocity is measured. At the manufacturer level, a conductive wire square is set up at two distances. The passage of the bullet through the square’s openings triggers timers to determine velocity.
How about attaching a fine piece of monofilament to the point of the tip, then hanging it vertically in a piece of tube and blowing air down the tube? Gravity is constant, the airspeed in the tube can be measured, so a strain gauge attached to the suspending line should measure something that is proportional to aerodynamic drag.
Might need to do something to get good laminar flow in the tube (blow the air into the top through a bundle of drinking straws)
That seems convoluted.
Why not just shoot the arrow and measure the drop?
Here’s my suggestion:
Hang the arrow from two strings and suspend it in front of a fan. Using two strings will remove the need for finding the center of gravity as well as keeping it pointed at the fan. When the fan is turned on, if all goes well, the arrow should arc up and back and find an equilibrium. The more drag it experiences, the further up the arc it will be pushed.
Assuming it works as I imagine it, as long as you don’t rearrange the set up, it would hopefully be consistent enough that you can tell if what you’re doing is helping or hurting your design.
One issue I see with this, which would also happen with a wind tunnel is you’re not taking into consideration the increased drag due to the arrow flexing as it flies. I have no idea what kind of relationship, if any, there would be between an arrow that’s flexing and an arrow that’s not.
Looking at it like that, what The Librarian said is probably the easiest. Shoot the arrow and see how far it goes. If you stand in the same place and pull the bow back the same amount, it should be fairly repeatable.
As I mentioned earlier, shooting a target arrow can be very consistent, shooting a flight arrow is an entirely different ballgame because they are so light and finicky. Drag is just one factor we like to isolate. You can’t isolate drag by shooting the arrow, you can tell the best arrow but that would most likely be because it came out of the bow cleanly.
This is what I am leaning toward. One of our engineers determined that there is not much advantage to shooting an arrow much faster than it’s terminal velocity, I am not sure I agree with this but determining the terminal velocity would be very useful. Suspending an arrow at it’s center of mass in a vertical tube and blowing up through the tube might give me a pretty good idea of its terminal velocity.
Make a wind tunnel. Round pipe, maybe 4" clear PVC pipe, a powerful fan like a leaf blower, and some kind of stator to remove turbulence.
Are there heads on these arrows or just ground down to points? How about fletching? Wouldn’t the head and the feathers be the greatest source of drag?
As suggested, operate this vertically. You can hang the arrow from a strain gauge with a thread to measure drag. You can introduce smoke trails into the chamber to observe air flow but you might do better info from gluing hair or silk threads to the shaft.
Has anyone looked for ways to achieve laminar flow on the arrow shaft? How about faired shafts instead of simple cylinders?
No weighted points, just ground down. The fletchings are small maybe 1/4" high by 1" long. A few years ago I had a water jet cutter slice water buffalo horn into .010 thicknesses and I used that for fletch, normally we use the thinnest feathers we can find and sometimes paper. It has to be a natural material no synthetics.
What would a stator look like in this application?
It will take quite a bit of experimentation to determine the right dimensions and uniform controllable flows. It’s not like anyone anywhere has ever done a DIY wind tunnel. I mean, you’d have to have common shop tools and off the shelf materials to build something like the picture below (which, as I said, no one anywhere has done, lot alone published detailed plans)
I think filling the space with tubes like in the picture above from @peccavi. Maybe smaller thinner wall stuff, don’t know if soda straws are too narrow. Since you’re looking at arrows you can use a narrow cylindrical tunnel. What air speeds are you looking at?
I am well aware that a wind tunnel can easily be built at home. I know several guys have played with it but I have never heard of any useful data coming out of it. That doesn’t mean they tried everything. I saw a video of a guy testing hobby rockets using a stick and string and that is where I got the idea.