Arrow Drop Variation Due to Mass Variation

[GrahameA]

Hi Dave

Well it intrigued me. Could not find the info on the site suggested so simplified the equations and built a spreadsheet.

The following results are for an arrow shot horizontally with target being 25m away. I have ignored drag, so the velocity is constant, and I have ignored any changes in the efficiency of the bow so the energy in the arrow is constant.

I started with a 500gn arrow at 45m/s - ie roughly 150fps.

As you can see every grain change causes the arrow to drop 3mm. So a 10 grain difference between arrow should result in the heavier arrow impacting 30mm (1 1/2") below the lighter. And it is losing about 40mm per second in velocity per each additional grain.

Ecuse the poor formating - the forum did want to co-operate and I have had enough for today.

Overall Arrow Mass
Drop m grains

0.003 501.0000
0.006 502.0000
0.009 503.0000
0.012 504.0000
0.015 505.0000
0.018 506.0000
0.021 507.0000
0.024 508.0000
0.027 509.0000
0.030 510.0000
0.033 511.0000
0.036 512.0000
0.039 513.0000
0.042 514.0000
0.045 515.0000
0.048 516.0000
0.051 517.0000
0.054 518.0000
0.058 519.0000
0.061 520.0000

[ed]

Thanks Graham,
that is enough to make me be more careful about matching my arrows.

3cm drop per 10 grains is a big enough difference to affect targetting, and so rather match the arrows better than adjust my shot each time.

[GrahameA]

Hi Ed

Those figures are for a range of 25m and an arrow velocity of 45 m/s with a 500gn arrow. If you go for a faster arrow then the amount of variation will decrease. And as the range increases it wil naturally increase.

Those figures do not take into drag but it is proportional to velocity squared. At short ranges I do think it is much of an issue but at longer ranges I have an inkling it may be noticeable.

Like you it has had some effect on my approach to to my target arrows - and bows. Shoot the fastest arrow you can taking into account all other factors.

I intend to redo the spreadsheet and make it a bit more friendly to use. When I have it done I will post it so people can use it.

[Mick Smith]

Hi Grahame

Thanks for the interesting figures. The arrow drop is more than what I would have expected. It stood to reason that major variations of arrow weight would effect the point of impact to a degree, but it really surprises me that the effect is so marked with only minor weight variations.

I've been very careful to weight match my timber arrows for years. I always thought I was doing it more for reasons of having confidence in my equipment rather than anything else, now it seems that I wasn't wasting my time and efforts at all.

Mick

[GrahameA]

Mick

Like you I was surprised at the figures. Make that stunned - stunned enough to redo all the equations because the figures were so surprising.

The cause is the velocity drop off and the increasing time of flight as the arrow energy remains constant.

My caveat would be that in the real world there should be an increase in bow efficiency so these would be worst case figures.

Even so it is food for thought and from now on I will be chasing much smaller differences for my own arrows - both wood and aluminium.

[Brumbies Country]

Mick

Like you I was surprised at the figures. Make that stunned - stunned enough to redo all the equations because the figures were so surprising.

The cause is the velocity drop off and the increasing time of flight as the arrow energy remains constant.

My caveat would be that in the real world there should be an increase in bow efficiency so these would be worst case figures.

Even so it is food for thought and from now on I will be chasing much smaller differences for my own arrows - both wood and aluminium.

Gee Grahame, those are interesting figures. That has big implications when shooting wood arrows froma longbow at maximum Fremantle target distance (60m). at max ABA distance (48m) and especially IFAA (80 yards). I guess those masters of the York round such as Horace Fordmade a point of matching arrows by weight. Joe Vardon, who is the best target longbower I have come across certainly sets a lot of store in matching spine and weight, though he reckons you can get away with a fair bit re straightness.

[GrahameA]

Hi BC

Yep. Matching the arrows probably pays higher benefits than straigntness. Now I have to learn how to trim shafts to match the weight without causing a large change in spine.

I have always been impressed by Ford. Even more so now. Will have to change my Avatar

[yeoman]

I heard of one person using wood arrows saoking them in finish/oil so that they had matched mass.

No need to change your avatar: the Chinese didn't measure spine at all, but arrow mass alone!

Dave

[greybeard]

Grahamea,
Did you actually shoot any arrows to arrive at the figures listed. On the surface they may look impressive but do they count for much. As you stated you disregarded certain factors. Surely to state these figures you must have carried them out in a controlled enviorment using a shooting machine. At the end of the day and facing the elements in the field does it count for much.
Daryl.

[GrahameA]

Hi Darryl

No. That is a ballistic simulation of the flight. As I said:

Well it intrigued me. Could not find the info on the site suggested so simplified the equations and built a spreadsheet.

All it does is show the difference in the amount of arrrow drop as the mass change between two arrows varies. No more no less

For real arrows the change in bow efficiency would decrease the variation as would the decrease in drag as the velocity decreases, drag being proportional the square of the velocity. However the difference would be small as the time of flight is short. On the other side due to the differences in individual shafts and the construction of individual arrows the variation between arrows would be increased.

I could have taken account the other factors but it gains little and once again it would only be a close approximation as the drag values would vary as the tip shape, nock shape and fletching changed.

To run an actual set of experiments we would need a shooting machine or someone to do a set of shots confirming the values. At the moment I am aware of only one such facility in Oz and it is privately owned and not yet fully operational.

If you are interested and would to read a bit more about this Bob Kooi's and Joe Tapley's work is a good start :

http://www.bio.vu.nl/thb/users/kooi/
http://homepage.ntlworld.com/joetapley/