Mythic Archery - Bow Efficiency & Ballistics Calculator

Bow & Arrow Setup Inputs

MODE: IMPERIAL

Arrow Mass / Weight 460 gr (29.8 g)

grains (gr)

Arrow Speed / Velocity 320 fps (97.5 m/s)

feet/sec (fps)

Bow Draw Weight 87.4 lbs (39.6 kg)

pounds (lbs)

Bow Draw Length 27.50 in (69.8 cm)

inches (in)

Brace Height 6.50 in (16.5 cm)

inches (in)

Cam Force-Draw Profile (k factor) Selected k = 0.82

Modern Aggressive Cam k=0.82 High-let-off binary or dual cams with steep draw force profile (k ≈ 0.82) Smooth Hybrid / Dual Cam k=0.77 Balanced draw curve with moderate force building (k ≈ 0.77) Solo / Single Cam k=0.72 Smooth linear draw stroke with soft transition into let-off (k ≈ 0.72) Recurve / Traditional k=0.5 No let-off, continuous force buildup up to full draw (k ≈ 0.50)

Custom Force Factor

k = 0.812

Setup Efficiency & Arrow Mass Insight

5.26 gpp

Speed setup (5.26 gpp): built for a flat trajectory. A little more arrow weight would make it quieter and more efficient.

5.26

Below IBO Speed All-round Heavy hunting

356.5811

Mass vs. speed trade-off: a heavier arrow leaves slower but absorbs more of the bow's stored energy, so it carries more kinetic energy and momentum and the shot is quieter. A lighter arrow gets there faster with a flatter trajectory, but leaves more energy in the bow as shock and noise.

Bow Energy & Efficiency Results

High Efficiency

Efficiency Factor 83.4% KE / Stored Energy

Share of the bow's stored energy converted into arrow kinetic energy.

Kinetic Energy 104.62 ft-lbs 141.85 Joules

Momentum 0.654 slug-ft/s 2.907 N·s

Stored Work 125.42 ft-lbs 1.44 ft-lb / lb draw

Arrow Weight Ratio 5.26 gpp 20.80 ft-lbs loss

Forecasted Velocity Chrono vault model Typical error ±11.5 fps | 4 records

Predicted initial speed

309 FPS

~94.2 m/s metric

vs entered speed -11.0 FPS (-3.4%)

Forecasted KE 97.6 ft-lbs 132.3 J

Forecasted momentum 0.631 slug-ft/s 2.81 N·s

Nearest benchmark Hoyt AX90 100% match · High Confidence

Dynamic Energy Partition & Transfer Curve

Stored 125.4 ft-lbs |83.4% to the arrow

Arrow absorbed: 104.6 ft-lbs (83.4%) Limb shock & sound loss: 20.8 ft-lbs (16.6%)

Kinetic transfer efficiency by arrow mass (350–650 gr) +1.8% efficiency per +100 gr

System absorption rule: heavier arrows stay on the string longer during the power stroke and turn more of the stored energy into forward motion. Lighter arrows leave faster but leave more energy behind as limb vibration, noise and hand shock. Modeled here as about +1.8% efficiency per extra 100 grains, the same rule as the mass chart.

Bow Velocity Forecaster

Predict arrow speed for a different draw weight, draw length or arrow, from a setup you've measured on a chronograph or from the chrono vault.

My measured setup Chrono vault

Benchmark setups

1. Your measured setup Use my calculator setup

Arrow mass gr Known speed fps Draw weight lbs Draw length in Brace height in

Enter a setup you've measured on a chronograph, or tick "Use my calculator setup".

1. Chrono vault model High Confidence

Typical error±11.5 fps

Prediction band±11.5 fps

Weighted efficiency77.6%

Records used4

Method: Local weighted mean (few nearby records). A sloped local fit needs about 15 similar records nearby; until then the forecast leans on a weighted average of the closest ones.

Closest vault records

Hoyt AX90 87.4# · 460 gr · 27.50" 320 fps100% match
Hoyt VTM 33 84.4# · 430 gr · 27.50" 302 fps89% match
Mathews Phase 4 29 75.0# · 422 gr · 27.00" 285 fps75% match

2. Setup to forecast

Draw weight

lbs

Arrow mass

gr

Draw length

in

Brace height

in

3. Forecast speed

320 fps

320.0 fps · 97.5 m/s

Kinetic energy104.6 ft-lbs

Momentum0.654 slug-ft/s

Efficiency83.4%

Arrow weight ratio5.26 gpp

Change from your measured setup

Draw weight 0.0 Draw length 0.0 Arrow mass 0.0 Combined 0.0 fps

Measured setup method: energy scales with draw weight and power stroke from the setup you measured, and efficiency rises about 1.8% per 100 grains of extra arrow weight.

Force-Draw Curve & True Efficiency

The area under a measured force-draw curve (trapezoidal rule, ∫ F dx) is the energy the bow really stores. It gives the true cam factor k and, with a chronographed arrow, true efficiency.

Pro staff review new curves

Export CSV

Draw force (lbs) by draw position (inches from brace height)

Total energy capacitance (ft-lbs) by draw position (inches)

Bow A

Hoyt VTM 33

HBX Pro Cam (84.4# Peak) · 27.50" draw · 6.500" brace · 43 readings

Peak weight84.4 lbsat 6.5"

Holding weight19.6 lbs76.8% let-off

Stored energy117.87 ft-lbs159.8 J · 1.40 per lb

True cam factork 0.798over a 21.0" power stroke

Arrow energy87.10 ft-lbs430 gr @ 302.0 fps

True efficiency73.9%30.77 ft-lbs lost to noise & vibration

Momentum0.577 slug-ft/s2.57 N·s

Virtual mass152 grlimbs, cams & string

Draw board load-cell data for Hoyt VTM 33. Peak draw weight 84.4 lbs @ 6.5" draw, 19.6 lbs holding weight @ 21.0" (76.8% let-off), 117.87 ft-lbs stored input energy (k = 0.798) across 21.0" power stroke.

Bow B

Hoyt AX90

Aggressive Cam (87.4# Peak) · 27.50" draw · 6.500" brace · 43 readings

Peak weight87.4 lbsat 5.5"

Holding weight23.6 lbs73.0% let-off

Stored energy124.27 ft-lbs168.5 J · 1.42 per lb

True cam factork 0.812over a 21.0" power stroke

Arrow energy104.62 ft-lbs460 gr @ 320.0 fps

True efficiency84.2%19.65 ft-lbs lost to noise & vibration

Momentum0.654 slug-ft/s2.91 N·s

Virtual mass86 grlimbs, cams & string

Draw board load-cell data for Hoyt AX90. Peak draw weight 87.4 lbs @ 5.5" draw, 23.6 lbs holding weight @ 21.0" (73.0% let-off), 124.27 ft-lbs stored input energy (k = 0.812) across 21.0" power stroke.

Head to head

Measure	Hoyt VTM 33	Hoyt AX90	B − A
Peak draw force	84.4 lbs	87.4 lbs	+3.0 lbs
Holding weight	19.6 lbs	23.6 lbs	+4.0 lbs
Let-off	76.8%	73.0%	-3.8%
Power stroke	21.0"	21.0"	—
Stored energy (∫ F dx)	117.87 ft-lbs	124.27 ft-lbs	+6.40 ft-lbs
Stored energy per lb of draw	1.397 ft-lb/lb	1.422 ft-lb/lb	+0.025 ft-lb/lb
Cam factor k	0.798	0.812	+0.014
Test arrow energy	87.10 ft-lbs	104.62 ft-lbs	+17.52 ft-lbs
True efficiency	73.9%	84.2%	+10.3%
Virtual mass	152 gr	86 gr	-66 gr

Other arrow weights

Projected from each bow's stored energy and virtual mass: efficiency = arrow / (arrow + virtual mass). Heavier arrows take more of the stored energy but leave slower.

Arrow	Hoyt VTM 33			Hoyt AX90
Arrow	Speed	KE	Efficiency	Speed	KE	Efficiency
350 gr	325 fps	82.2 ft-lbs	69.7%	358 fps	99.8 ft-lbs	80.3%
400 gr	310 fps	85.4 ft-lbs	72.5%	339 fps	102.3 ft-lbs	82.3%
450 gr	297 fps	88.1 ft-lbs	74.8%	323 fps	104.3 ft-lbs	84.0%
500 gr	285 fps	90.4 ft-lbs	76.7%	309 fps	106.0 ft-lbs	85.3%
550 gr	275 fps	92.3 ft-lbs	78.3%	297 fps	107.5 ft-lbs	86.5%
600 gr	266 fps	94.0 ft-lbs	79.8%	286 fps	108.7 ft-lbs	87.5%
650 gr	257 fps	95.5 ft-lbs	81.0%	276 fps	109.7 ft-lbs	88.3%

Show the readings as a table

Hoyt VTM 33 draw	Force	Stored so far	Hoyt AX90 draw	Force	Stored so far
0.00"	0.0 lbs	0.00 ft-lbs	0.00"	0.0 lbs	0.00 ft-lbs
0.50"	10.4 lbs	0.22 ft-lbs	0.50"	8.8 lbs	0.18 ft-lbs
1.00"	19.5 lbs	0.84 ft-lbs	1.00"	16.0 lbs	0.70 ft-lbs
1.50"	27.6 lbs	1.82 ft-lbs	1.50"	24.2 lbs	1.54 ft-lbs
2.00"	36.0 lbs	3.15 ft-lbs	2.00"	33.6 lbs	2.74 ft-lbs
2.50"	47.0 lbs	4.88 ft-lbs	2.50"	47.0 lbs	4.42 ft-lbs
3.00"	57.4 lbs	7.05 ft-lbs	3.00"	56.6 lbs	6.58 ft-lbs
3.50"	67.4 lbs	9.65 ft-lbs	3.50"	69.0 lbs	9.20 ft-lbs
4.00"	76.0 lbs	12.64 ft-lbs	4.00"	78.4 lbs	12.27 ft-lbs
4.50"	81.0 lbs	15.91 ft-lbs	4.50"	83.0 lbs	15.63 ft-lbs
5.00"	83.4 lbs	19.33 ft-lbs	5.00"	85.6 lbs	19.14 ft-lbs
5.50"	84.2 lbs	22.83 ft-lbs	5.50"	87.4 lbs	22.75 ft-lbs
6.00"	84.2 lbs	26.33 ft-lbs	6.00"	87.2 lbs	26.38 ft-lbs
6.50"	84.4 lbs	29.85 ft-lbs	6.50"	86.6 lbs	30.00 ft-lbs
7.00"	84.2 lbs	33.36 ft-lbs	7.00"	85.8 lbs	33.60 ft-lbs
7.50"	84.0 lbs	36.86 ft-lbs	7.50"	85.8 lbs	37.17 ft-lbs
8.00"	82.6 lbs	40.33 ft-lbs	8.00"	84.8 lbs	40.73 ft-lbs
8.50"	82.8 lbs	43.78 ft-lbs	8.50"	83.6 lbs	44.23 ft-lbs
9.00"	83.4 lbs	47.24 ft-lbs	9.00"	83.2 lbs	47.71 ft-lbs
9.50"	83.0 lbs	50.71 ft-lbs	9.50"	84.8 lbs	51.21 ft-lbs
10.00"	83.0 lbs	54.17 ft-lbs	10.00"	85.8 lbs	54.76 ft-lbs
10.50"	83.0 lbs	57.63 ft-lbs	10.50"	86.2 lbs	58.35 ft-lbs
11.00"	82.8 lbs	61.08 ft-lbs	11.00"	86.8 lbs	61.95 ft-lbs
11.50"	83.2 lbs	64.54 ft-lbs	11.50"	86.8 lbs	65.57 ft-lbs
12.00"	83.2 lbs	68.00 ft-lbs	12.00"	86.4 lbs	69.18 ft-lbs
12.50"	83.0 lbs	71.47 ft-lbs	12.50"	86.4 lbs	72.78 ft-lbs
13.00"	82.8 lbs	74.92 ft-lbs	13.00"	86.2 lbs	76.37 ft-lbs
13.50"	81.8 lbs	78.35 ft-lbs	13.50"	86.2 lbs	79.96 ft-lbs
14.00"	80.6 lbs	81.73 ft-lbs	14.00"	86.0 lbs	83.55 ft-lbs
14.50"	79.6 lbs	85.07 ft-lbs	14.50"	85.4 lbs	87.12 ft-lbs
15.00"	78.0 lbs	88.35 ft-lbs	15.00"	85.0 lbs	90.67 ft-lbs
15.50"	76.4 lbs	91.57 ft-lbs	15.50"	84.0 lbs	94.19 ft-lbs
16.00"	74.6 lbs	94.72 ft-lbs	16.00"	82.8 lbs	97.67 ft-lbs
16.50"	72.6 lbs	97.78 ft-lbs	16.50"	81.4 lbs	101.09 ft-lbs
17.00"	70.2 lbs	100.76 ft-lbs	17.00"	79.4 lbs	104.44 ft-lbs
17.50"	67.0 lbs	103.62 ft-lbs	17.50"	77.2 lbs	107.70 ft-lbs
18.00"	63.4 lbs	106.33 ft-lbs	18.00"	74.2 lbs	110.85 ft-lbs
18.50"	59.6 lbs	108.90 ft-lbs	18.50"	70.4 lbs	113.87 ft-lbs
19.00"	54.8 lbs	111.28 ft-lbs	19.00"	64.4 lbs	116.68 ft-lbs
19.50"	49.2 lbs	113.45 ft-lbs	19.50"	56.0 lbs	119.18 ft-lbs
20.00"	42.0 lbs	115.35 ft-lbs	20.00"	47.0 lbs	121.33 ft-lbs
20.50"	29.8 lbs	116.84 ft-lbs	20.50"	35.2 lbs	123.04 ft-lbs
21.00"	19.6 lbs	117.87 ft-lbs	21.00"	23.6 lbs	124.27 ft-lbs

Kinetic Energy & Game Penetration Scale

Target output: 104.62 ft-lbs

Small Game

< 25 ft-lbs

Target species

Rabbits
Squirrels
Small Game Birds
Target Practice

Ideal for target shooting and small varmint hunting.

Medium Game

25 – 41 ft-lbs

Target species

Whitetail Deer
Antelope
Wild Boar (Small)

Pass-through potential on white-tailed deer with razor sharp broadheads.

Large Game

41 – 65 ft-lbs

Target species

Elk
Black Bear
Moose
Caribou
Large Wild Boar

Exceptional kinetic punch for North American big game.

Tough / Dangerous Game

> 65 ft-lbs

Target species

Grizzly / Brown Bear
Cape Buffalo
Giraffe
Bison

Maximum penetration momentum for heavy bone and thick hide.

Penetration physics note: kinetic energy measures overall work capacity (KE = ½ × m × v²), while arrow momentum (p = m × v = 0.654 slug-ft/s) governs pass-through in heavy muscle and bone. Razor-sharp broadheads make the most of that momentum.

Arrow FOC & Component Mass Builder

Front-of-center balance and total arrow weight from your components, or from a measured balance point.

Component build Measured balance

Component presets

Shaft cut length

in

Shaft mass (GPI)

gr/in

Point / broadhead

gr

Insert / HIT / outsert

gr

Footing collar / sleeve

gr

Vanes

gr each

Arrow wrap / crest

gr

Nock + bushing

gr

How to measure (AMO method)

Measure the arrow from the throat of the nock (where the string sits) to the end of the shaft, not the point.
With point, vanes and nock installed, balance the arrow on a thin edge and mark the balance point.
Measure from the nock throat to that mark.

Arrow length

in

Nock throat to balance point

in

Front of center

10.4%

Target / Field

Total arrow weight

435.2 gr

28.2 g · shaft 269.7 gr

Arrow length29.00 in

Nock to balance17.51 in

Offset from center+3.01 in

Geometric center14.50 in

Recommendation: Ideal for flat-trajectory indoor target shooting and Olympic recurves with field points.

Radar Telemetry & Ballistics

Enter downrange radar speeds to measure your arrow's drag, then see speed, energy, drop and wind drift out to 100 yards.

Known setups

1. Radar readings

Launch speed (at the bow) fps

DistanceRadar speed

yd fps

2. Arrow & air

Shaft diameter Arrow mass gr Temperature °F Altitude ft Station pressure inHg Humidity %

Station pressure is the actual barometer reading where you shoot, not the sea-level value in weather reports.

3. Measured drag Fit R² 1.000

Speed lost per 10 yd8.6 fps

Drag coefficient10.46

Ballistic coeff.0.0055

Sectional density2.385 lb/in²

Distance	Radar	Model
20 yd	308.0 fps	308.1 fps
40 yd	292.0 fps	292.0 fps
60 yd	277.0 fps	276.8 fps

Air density 1.194 kg/m³ (97.5% of standard) Density altitude 2,730 ft Speed of sound 1,128 fps

4. Downrange flight, 0–100 yards

Sight zero yd Crosswind mph Sight height in

Inspect range: 40 yd

Speed at 40 yd292.0 fps89.9% kept

Kinetic energy87.1 ft-lbs80.7% kept · Tough / Dangerous Game

Impact vs 20 yd pin-11.9 inbelow the pin · flight 390 ms

10 mph crosswind3.6 in driftmomentum 0.596 slug-ft/s

Arrow height relative to the 20 yd pin (inches) by distance (yards)

Range	Speed	Kept	KE	Momentum	Time	vs 20 yd pin	10 mph drift	Game tier
0 yd 0 m	325.0 fps	100.0%	107.9 ft-lbs	0.664	0 ms	-3.5"	0.0"	Tough / Dangerous Game
10 yd 9 m	316.4 fps	97.4%	102.3 ft-lbs	0.646	94 ms	0.0"	0.2"	Tough / Dangerous Game
20 yd 18 m Zero	308.1 fps	94.8%	97.0 ft-lbs	0.629	190 ms	0.0"	0.9"	Tough / Dangerous Game
30 yd 27 m	299.9 fps	92.3%	91.9 ft-lbs	0.613	288 ms	-3.9"	2.0"	Tough / Dangerous Game
40 yd 37 m	292.0 fps	89.9%	87.1 ft-lbs	0.596	390 ms	-11.9"	3.6"	Tough / Dangerous Game
50 yd 46 m	284.3 fps	87.5%	82.6 ft-lbs	0.581	494 ms	-24.5"	5.7"	Tough / Dangerous Game
60 yd 55 m	276.8 fps	85.2%	78.3 ft-lbs	0.565	601 ms	-41.8"	8.3"	Tough / Dangerous Game
70 yd 64 m	269.5 fps	82.9%	74.2 ft-lbs	0.550	711 ms	-64.4"	11.3"	Tough / Dangerous Game
80 yd 73 m	262.4 fps	80.7%	70.3 ft-lbs	0.536	823 ms	-92.6"	15.0"	Tough / Dangerous Game
90 yd 82 m	255.5 fps	78.6%	66.7 ft-lbs	0.522	939 ms	-126.8"	19.1"	Tough / Dangerous Game
100 yd 91 m	248.7 fps	76.5%	63.2 ft-lbs	0.508	1,058 ms	-167.5"	23.8"	Large Game

How this is modeled: one drag value fitted to your radar readings, gravity, and a launch angle that puts the arrow on the pin at your zero distance. Wind drift uses Didion's formula for a steady crosswind at 90°. Real flight also depends on tune, broadhead and gusts, so confirm long shots on the range.

Arrow Mass Sensitivity & Efficiency

How speed, kinetic energy and efficiency change if you shoot a lighter or heavier arrow from this bow.

Kinetic energy Velocity Efficiency Momentum

Your current arrow Other arrow weights

Kinetic energy (ft-lbs) by arrow mass (gr)

Arrow speed (fps) by arrow mass (gr)

Bow efficiency (%) by arrow mass (gr)

Momentum (slug-ft/s) by arrow mass (gr)

Show as table

Arrow (gr)	Speed (fps)	KE (ft-lbs)	Efficiency	Momentum (slug-ft/s)
275	405.5	100.4	80.1%	0.495
300	389.3	101.0	80.5%	0.519
325	375.1	101.6	81.0%	0.541
350	362.4	102.1	81.4%	0.563
375	351.1	102.7	81.9%	0.585
400	340.9	103.2	82.3%	0.605
425	331.6	103.8	82.8%	0.626
450 (current)	323.2	104.4	83.2%	0.646
475	315.4	104.9	83.7%	0.665
500	308.2	105.5	84.1%	0.684
525	301.6	106.1	84.6%	0.703
550	295.5	106.6	85.0%	0.722
575	289.7	107.2	85.5%	0.740
600	284.4	107.8	85.9%	0.758
625	279.3	108.3	86.4%	0.775
650	274.6	108.9	86.8%	0.793
675	270.2	109.5	87.3%	0.810
700	266.0	110.0	87.7%	0.827

How this is modeled: the bow's stored energy stays fixed, and efficiency rises about 1.8% for every 100 grains of added arrow weight (limited to 45–92%). Heavier arrows leave the string slower but carry more of the limb energy, so they hit harder and shoot quieter.

Saved Setups & Comparator

Side-by-side comparison

Tick Compare on up to 4 saved setups below to see them side by side with your current inputs.

Setup	Arrow	Speed	Draw wt / length	GPP	Kinetic energy	Momentum	Efficiency	Game tier
Current setup	460 gr	320 fps	87.4 lb / 27.50"	5.26	104.6 ft-lbs	0.654 slug-ft/s	83.4%	Tough / Dangerous Game

Your setups

Move setups between browsers without an account:

Chronograph Vault 4 in use Measured chronograph readings that power the velocity forecasts, with a physics check on every entry

Used by forecasts 4 of 4 records

Model accuracy ±11.5 fps typical error LOWESS · physics check 45–92.5% efficiency

Moderation New readings are reviewed Pro staff sign in to approve submissions.

Export JSON

Bow	Draw wt × length	Arrow	Speed	KE	Efficiency	Status	Model check
Hoyt AX90 Garmin Xero C1 Pro Radar · 2026 Hoyt AX90: 87.4# draw weight, 21.0" power stroke (27.5" DL @ 6.5" brace), 460gr arrow, 320 fps exit velocity. Aggressive cam (k = 0.812, 124.3 ft-lbs stored).	87.4# @ 27.50"6.50" brace	460 gr5.3 gpp	320 fps	104.6 ft-lbs	83.4%IBO ~333	Lab verified	+18.4 fps weight 1.00
Hoyt VTM 33 Garmin Xero C1 Pro Radar · 2023 Hoyt VTM 33: 84.4# draw weight, 21.0" power stroke (27.5" DL @ 6.5" brace), 430gr arrow, 302 fps exit velocity. HBX Pro cam (k = 0.798, 117.9 ft-lbs stored).	84.4# @ 27.50"6.50" brace	430 gr5.1 gpp	302 fps	87.1 ft-lbs	76.6%IBO ~315	Lab verified	-1.7 fps weight 1.00
Hoyt Faktor 30 Garmin Xero C1 Pro Radar · 2024 Hoyt Faktor 30: 65# draw weight, 29" draw length, 430gr arrow, 259 fps exit velocity. Smooth hybrid cam.	65.0# @ 29.00"6.75" brace	430 gr6.6 gpp	259 fps	64.1 ft-lbs	69.0%IBO ~318	Lab verified	-4.7 fps weight 1.00
Mathews Phase 4 29 Garmin Xero C1 Pro Radar · 2024 Mathews Phase 4 29: 75# draw weight, 27" draw length, 422gr arrow, 285 fps exit velocity. Aggressive cam.	75.0# @ 27.00"6.00" brace	422 gr5.6 gpp	285 fps	76.1 ft-lbs	70.7%IBO ~330	Lab verified	-12.9 fps weight 1.00

Archery Physics & Formula Reference Guide Kinetic energy, stored work and bow efficiency calculations

1. Arrow Kinetic Energy (KE)

The total work the arrow can deliver on impact:

KE (ft-lbs) = (arrow mass in grains × velocity in fps²) / 450,240

450,240 = 2 × 7,000 grains/lb × 32.16 ft/s², the archery-industry standard constant.

2. Arrow Momentum (p)

Resistance to deceleration; correlates with penetration through dense tissue and bone:

Momentum (slug-ft/s) = (arrow mass in grains × velocity in fps) / 225,218

225,218 = 7,000 grains/lb × 32.174 ft/s². 1 slug-ft/s = 4.448 N·s.

3. Stored Potential Work (Input Energy)

Energy stored in the limbs as the string is drawn to full draw:

Stored energy (ft-lbs) = k × draw weight (lbs) × [(draw length − brace height) / 12]

k is the force-draw profile multiplier. Modern compound cams hold near peak weight across the power stroke, giving k ≈ 0.78–0.84.

4. Efficiency Factor (η)

How much of the stored limb energy becomes arrow kinetic energy:

Efficiency (%) = [arrow KE (ft-lbs) / bow stored energy (ft-lbs)] × 100

Energy not transferred to the arrow goes into limb vibration, cam noise, string friction and hand shock.

5. Probable Velocity Estimation Model

Estimates arrow speed when draw weight, draw length or arrow weight change from a known reference setup:

KE_target = KE_ref × (DW_target / DW_ref) × (PS_target / PS_ref) × [1 + (Δm / 100) × 1.8%]

Velocity is then v = √(KE_target × 450,240 / m_target), including the efficiency gain from heavier arrows (+1.8% per +100 gr).

6. Force-Draw Integration & True Efficiency (Trapezoidal Rule)

With draw force measured at high resolution (e.g. every 0.5" of a 21.0" power stroke), input energy is the area under the force-draw curve:

E_in (ft-lbs) = ∫ F(x) dx ≈ Σ [ (F_i + F_i+1) / 2 × (Δx_inches / 12) ] k_true = E_in / [peak draw weight (lbs) × power stroke (ft)]

True efficiency is η_true = (arrow KE / E_in) × 100. Hoyt VTM 33 (84.4#): k ≈ 0.798, E_in = 117.9 ft-lbs. Hoyt AX90 (87.4#): k ≈ 0.812, E_in = 124.3 ft-lbs.

7. Chrono Vault Forecast (LOWESS)

Each vault record's measured efficiency is computed with its own cam factor:

η_i = KE_i / (k_cam,i × DW_i × PS_i / 12)

For a new setup, the nearest 75% of records (at least 5) are weighted by the tricube kernel of their distance in (draw weight, power stroke, grains per pound, arrow mass), times a data-quality weight (lab 1.0, pro 0.85, approved user 0.6, fewer shots less). A weighted local line through their η gives the prediction:

w_i = q_i × (1 − (d_i/h)³)³ · v = √(η̂ × k × DW × PS/12 × 450,240 / m)

With few nearby records the line is blended toward the weighted mean. Accuracy is reported as the leave-one-out typical error: each record predicted from all the others.

Mythic Archery Ballistics & DFC

Navigation Index

Bow & Arrow Setup Inputs

Setup Efficiency & Arrow Mass Insight

Bow Energy & Efficiency Results

Dynamic Energy Partition & Transfer Curve

Bow Velocity Forecaster

Force-Draw Curve & True Efficiency

Add a bow's force-draw curve

Hoyt VTM 33

Hoyt AX90

Head to head

Other arrow weights

Kinetic Energy & Game Penetration Scale

Arrow FOC & Component Mass Builder

Radar Telemetry & Ballistics

Arrow Mass Sensitivity & Efficiency

Saved Setups & Comparator

Side-by-side comparison

Your setups

Submit a chronograph reading

1. Arrow Kinetic Energy (KE)

2. Arrow Momentum (p)

3. Stored Potential Work (Input Energy)

4. Efficiency Factor (η)

5. Probable Velocity Estimation Model

6. Force-Draw Integration & True Efficiency (Trapezoidal Rule)

7. Chrono Vault Forecast (LOWESS)