Spine Arrow Calculator
Please complete the following information. We will then be able to provide you with the recommended spine value.
In a nutshell
- Arrow spine: the deflection of a shaft in thousandths of an inch, measured to ASTM F2031 with a 1.94 lbs (880 g) load over a 28 inch (711 mm) span. A 500 spine deflects 0.500 inches (12.7 mm) and is weaker than a 400.
- Spine chart: 30 to 35 lbs on the fingers calls for roughly 700 to 600 spine, 40 to 45 lbs for 500 to 450, and anything above 55 lbs for 340 to 300. Reference values are 28 inch arrow length and a 100 grain point.
- Rules of thumb: one extra inch of arrow length acts like 5 lbs less draw weight, and so does 20 to 25 grain more point weight. Both make the arrow behave weaker.
- Bow type: longbows need roughly 10 lbs weaker than the chart value, recurve bows follow the manufacturer chart, and compound bows shot with a release are better off one step stiffer.
- Material: carbon and aluminium follow the ASTM standard, while wooden arrows are measured over a 26 inch span with a 2 lbs load and labelled in pounds, for example 40 to 45 lbs.
- Diagnosis: a weak arrow pushes right for a right-handed archer, a stiff one pushes left. A bare shaft at 15 to 20 yards (14 to 18 m) tells you which it is within three arrows.
What is arrow spine?
Arrow spine describes how far an arrow shaft bends under a standardised load. The measurement follows ASTM F2031, the standard used by most manufacturers. A 29 inch shaft without point or nock rests on two supports spaced 28 inches (711 mm) apart, a weight of 1.94 lbs (880 g) is applied at the centre, and the deflection is read in thousandths of an inch. If the shaft deflects 0.500 inches, it is a 500 spine.
That gives you a scale which trips up almost everyone at first. The higher the number, the weaker the arrow. A 700 spine is considerably weaker than a 340, and a 300 sits among the stiffest shafts on the market. If your instinct says a bigger number means a stronger arrow, your instinct has it exactly backwards.
Spine is therefore not a quality rating, it is a fit. It has to match your draw weight, your draw length, your point weight and your bow type. That combination is exactly what the calculator above works out for you.
Arrow spine chart for carbon and wood
The chart below gives reference values for carbon shafts at 28 inch arrow length with a 100 grain point. What counts is the draw weight you actually hold on your fingers, not the number printed on the limb. With a longer draw, real weight often sits 5 to 10 lbs above the marked figure.
| Draw weight on the fingers | Carbon spine (28 inch, 100 grain) | Wooden arrow rating |
|---|---|---|
| 15 to 20 lbs | 1300 to 1000 | 20 to 25 lbs |
| 20 to 25 lbs | 1000 to 900 | 25 to 30 lbs |
| 25 to 30 lbs | 900 to 700 | 30 to 35 lbs |
| 30 to 35 lbs | 700 to 600 | 35 to 40 lbs |
| 35 to 40 lbs | 600 to 500 | 40 to 45 lbs |
| 40 to 45 lbs | 500 to 450 | 45 to 50 lbs |
| 45 to 50 lbs | 450 to 400 | 50 to 55 lbs |
| 50 to 55 lbs | 400 to 340 | 55 to 60 lbs |
| 55 to 60 lbs | 340 to 300 | 60 to 70 lbs |
| above 60 lbs | 300 to 250 | above 70 lbs |
Two notes on the chart. It applies to bows cut to centre or close to it, which covers most carbon arrows on a recurve bow. And it is a starting point, not a verdict. If your figure lands right on the border between two spine values, point weight decides which step you take.
What the calculator needs from you
The calculator works with six figures. The more precisely you know them, the more you can trust the result.
- Draw weight in pounds, measured at your anchor point. A bow scale costs very little and gives you the honest number. Any decent pro shop will also measure it for free.
- Draw length in inches. If you do not know yours, our archery calculator works it out from your wingspan.
- Arrow length, normally around one inch longer than your draw length. That safety margin keeps the point from slipping behind the rest.
- Point weight in grains. 100 grain (6.5 g) is standard for target shooting, while 125 to 150 grain is common for 3D and field.
- Shaft material, because carbon, aluminium and wood use different measuring standards and different ranges.
- Bow type and string material, since a longbow on a Dacron string asks for a different spine than a compound bow shot with a release.
Static and dynamic spine
The number printed on the packaging is always static spine, the laboratory figure. In the shot the arrow behaves differently, because length, point weight, nock and fletching all join in. That behaviour is called dynamic spine, and two rules of thumb cover most of it.
| Change | Effect on dynamic spine | Roughly equivalent to |
|---|---|---|
| Arrow one inch longer | weaker | 5 lbs less draw weight |
| Point 20 to 25 grain heavier | weaker | 5 lbs less draw weight |
| Arrow one inch shorter | stiffer | 5 lbs more draw weight |
| Switch from Dacron to Fast Flight | calls for a stiffer shaft | about half a spine step |
In practice that means you can fine tune an arrow without buying new shafts. If your 500 spine flies marginally weak, a 100 grain point instead of a 125 brings it back into the window. We stock arrow points individually in a range of weights so you can test rather than guess.
Spine for recurve, longbow and compound
Not every bow puts the same demand on the arrow. The reason lies in the sight window and in how the string is released.
| Bow type | Characteristic | Correction to the chart value |
|---|---|---|
| Longbow and horse bow | arrow sits well off the centre line, strong archer's paradox | calculate around 10 lbs weaker |
| Recurve bow with a plunger | close to centre shot, fine tuning through the plunger | take the chart value |
| Compound bow with a release | centre shot, almost no sideways input from the fingers | go one step stiffer if in doubt |
| Compound bow shot with fingers | sideways input as on a recurve | chart value up to one step weaker |
On a longbow the effect is most pronounced and the tolerance widest. Shoot a shaft that is too stiff there and you see it on the target face immediately, because the arrow cannot swing cleanly around the grip. On a compound bow with a release, spine matters less. It still matters.
Spine in carbon, aluminium and wooden arrows
Shaft material decides how stable spine stays over time. Carbon arrows and carbon shafts hold their value indefinitely, stay light and keep their form. A damaged carbon shaft has to come out of the set, though, because it can splinter. Flex it gently before every shot and look for lifting fibres, which takes two seconds.
Aluminium arrows are exceptionally straight and remain a classic in indoor target archery. Spine notation works differently on the Easton XX75 series, where a four digit number gives diameter and wall thickness. A 2315 has a 23/64 inch outside diameter and a 0.015 inch wall. One bad shot into a hard backstop bends the shaft permanently, and then it is out of the set.
Wooden arrows follow the classic standard, measured over a 26 inch span with a 2 lbs load and usually labelled as a draw weight range such as 40 to 45 lbs. Wood reacts to humidity and temperature, so spine varies more within a set than it does with carbon. For traditional shooting that is part of the appeal. For competition it is a drawback, which is why World Archery target lines are dominated by carbon and aluminium.
How to spot the wrong spine
An arrow that does not match the bow leaves the string at an angle. On release, shaft and point compress, the arrow starts to oscillate and has to bend its way around the grip. That effect is called archer's paradox. Ideally the arrow has completed one full oscillation cycle by the time it leaves the string. If spine is off, residual oscillation carries into flight.
| What you see (right-handed archer) | Likely cause | Next step |
|---|---|---|
| Groups consistently right | arrow too weak, spine number too high | stiffer shaft or lighter point |
| Groups consistently left | arrow too stiff, spine number too low | weaker shaft or heavier point |
| Arrow wags sideways (fishtailing) | spine does not match the draw weight | bare shaft test at 15 to 20 yards |
| Arrow porpoises up and down | nocking point height, not spine | move the nocking point in small steps |
The bare shaft test is the most honest check you have. Shoot one unfletched shaft alongside your fletched arrows at 15 to 20 yards (14 to 18 m). If the bare shaft lands off to one side or sits at an angle in the target, spine is your issue. If it lands above or below the group, you are working on the nocking point. Before you change anything, check your form, because an inconsistent release produces the same patterns as the wrong shaft.
One point belongs under safety. A shaft that is far too weak can fail on a heavy bow, in the worst case at the moment of release. If you are sitting between two steps and genuinely unsure, take the stiffer one.
Reading manufacturer figures correctly
A spine number only compares within its own system, and this is where most wrong purchases happen. Easton, Gold Tip and most European brands use the standard scale, where 500 means 0.500 inches of deflection and low numbers mean stiff shafts. Carbon Express inverts the logic, so a 250 is weaker than a 350. A Maxima Red 250 deflects around 0.417 inches, a 350 only about 0.342 inches.
Practically speaking, never compare two numbers from two catalogues. Compare the deflection figure or the stated Easton equivalent. Every one of our complete arrows and carbon shafts carries the spine value on the variant, so you can map your calculator result straight onto a product. If you are torn between two options, drop us a message. We shoot ourselves, and we will also tell you when a shaft is the wrong call for your setup.
The arrow flight calculator
DownloadOnce spine is settled, trajectory is the next question. The arrow flight calculator works out the flight parabola and the theoretical range of your arrow. Enter draw weight, arrow weight, launch speed and angle, and you get the curve for your setup. The full calculation method with all formulas sits below the video.
Kindly provided by Markus
How the arrow flight calculator works
The calculator simulates arrow flight in small time steps. In every step it recalculates two forces, gravity and drag. The resulting acceleration gives the velocity for the next step, and from that comes the flight parabola. The formulas below are the basis of that calculation.
Drag
Drag depends on air density, arrow velocity, drag coefficient and frontal area. It always acts directly against the direction of flight and can be split into a horizontal and a vertical component.
- FFS = 1/2 * ρ * v² * C * A
The deceleration produced by drag additionally depends on the mass of the arrow.
- F = m * a
- a = F / m
- aS = 1/2 * ρ * v² * C * A / m
Because air density, drag coefficient, frontal area and mass all stay constant within one setup, they can be combined into a single factor k. After that, one multiplication per time step is enough.
- k = 1/2 * ρ * C * A / m
- aS = k * v²
| Symbol | Meaning | Unit and reference value |
|---|---|---|
| FFS | drag as a force | newtons |
| ρ | air density | kg/m³, around 1.225 at sea level and 59 °F (15 °C), which is 0.0765 lb/ft³ |
| v | arrow velocity | m/s, typically 50 to 90 in target archery, which is 165 to 295 fps |
| C | drag coefficient, see the section below | dimensionless |
| A | frontal area of the shaft | m² |
| m | mass of the complete arrow | kg, 1 grain equals 0.0648 g |
| a | acceleration | m/s² |
| aS | deceleration caused by drag | m/s² |
| k | combined factor from ρ, C, A and m | 1/m |
Four relationships follow from those formulas, and you can use all of them on the shooting line without a calculator.
- Thick arrows with a large frontal area experience more drag than slim shafts.
- Drag rises with the square of velocity. An arrow travelling twice as fast meets four times the braking force.
- Arrows with unfavourable aerodynamics, such as large feathers, flu flu fletching or non aerodynamic points, slow down considerably faster.
- Heavy arrows lose less speed than light ones, because their momentum is higher.
Drag coefficient
The calculator works with the frontal area of the shaft and represents the fletching through the drag coefficient. Small, straight feathers give a low coefficient, large and sweeping feathers a high one.
| Arrow type | Drag coefficient |
|---|---|
| Target arrow with small, straight fletching | around 2.1 |
| Arrow with large, sweeping fletching | well above 2.1 |
| LARP arrow | up to 45 |
An alternative approach is to work with the combined frontal area of shaft, fletching and every other component, using a constant drag coefficient of around 0.9 for an arrow shaped object. Both routes give similar results. The first one is easier to maintain in the spreadsheet.
Forces and accelerations acting on the arrow
Horizontally there is only one force. The arrow is slowed by the horizontal component of drag, and nothing else happens in that direction.
Vertically it splits in two. During the climb, before the apex, the vertical component of drag and gravity brake the arrow together. After the apex, drag reverses direction and acts as lift, slowing the descent while gravity keeps accelerating the arrow. Once lift and gravity balance out, the arrow continues at a constant speed. That is terminal velocity in free fall.
Limits of the model
The spreadsheet models a complex aerodynamic phenomenon, and plenty of real world effects cannot be captured in it. The underlying literature is listed under sources below. These effects are not accounted for.
- effects of attitude in flight and the changing frontal area that comes with it, particularly at extreme FOC, meaning a strongly forward weighted balance point
- effects of unstable attitude and strongly varying frontal area, particularly fishtailing or heavy oscillation
- drag coefficients that deviate, as with LARP arrows, flu flu fletching, strongly helical or unusual fletching
- changes to laminar or turbulent flow behaviour, for instance through altered surfaces
- changes to flow behaviour caused by unusual point shapes or nocks
- effects of arrow rotation and the Magnus forces it produces
For practical purposes that means the calculated curve is a very good approximation for target arrows with normal fletching. With flu flu arrows or extreme setups, reality drifts further away.
Sources
- Drag Coefficients of Bullets, Arrows, and Spears, Technical Archery
- Aerodynamic properties of an arrow, influence of point shape on the boundary layer transition, Procedia Engineering, ScienceDirect
- Arrow Aerodynamics, Capgo Flying Sticks
- Pfeil-und-Bogen-kaufen.de