Field Notes

Your bow is an energy source. What four chrono sessions taught the formula.

A new 454-grain build read 8.5 fps low on a freshly calibrated formula. The fix wasn't a new constant — it was a new model.

David Marcus · June 2026

After the draw-weight recalibration, I thought the FPS estimate was about done. My two heaviest builds were landing within 0.3 fps of the chronograph — about as tight as a specs-only formula gets. Then I finished a new, lighter build and put it through the Garmin Xero.

Flatline — a 454.6-grain build — chrono'd at 306.5 fps. The app estimated 298. That's −8.5 fps, the worst error I'd recorded, on a formula I had calibrated days earlier.

And here's the part that mattered: lined up light-to-heavy, the errors across all four builds weren't noise. They were a curve — −8.5, −6.6, −1.1, −0.7. A straight-line formula can't produce a curved residual. The constants weren't wrong. The model was.

What the chronograph was actually saying

Every speed formula I'd used treated arrow weight as a linear penalty: so many fps lost per grain. But when I put the four sessions side by side and looked at kinetic energy instead of speed, the pattern jumped out:

Across a 93-grain spread, speed drops 24 fps — but energy barely moves. The bow doesn't deliver speed. It delivers energy, roughly the same amount every shot, and speed simply falls out of the physics: v = √(E/m). Cut the mass, the speed climbs along a square-root curve. Speed-per-grain is a line; physics is a curve. That's why the linear formula tracked the heavy builds and drifted further off the lighter the arrow got.

Look closer and there's a second signal: energy creeps up with arrow weight — 94.8 to 97.2 ft·lb. Heavier arrows extract more from the bow, because they keep the limbs loaded longer through the power stroke. The chronograph data shows it directly.

The new model

So the formula was rebuilt around energy. It still starts from the same published inputs — IBO speed, draw weight, draw length, string accessories — but instead of marching fps up and down a line, it estimates how much energy the bow delivers and converts that to speed at your actual arrow weight:

In plain English: estimate the bow's IBO-condition speed for your setup (step 1), convert it to the energy a real bow actually delivers with a 350-grain arrow — 93% of the lab-ideal number (step 2), credit heavier arrows the extra energy they extract at 0.024 ft·lb per grain (step 3), and convert energy back to speed at your arrow's weight (step 4).

The results

All four builds inside ±0.9 fps. The lightest build — the one that broke the old model — went from −8.5 to −0.5. And because the curve is now the right shape, the formula degrades gracefully outside the tested range instead of drifting further with every grain.

A satisfying cross-check

One more thing the Garmin data confirmed: ArrowForge's kinetic-energy math is exact. The app computes KE as weight × speed² ÷ 450,240 — plug in shot #1 of the Flatline session (454.6 gr at 306.0 fps) and you get 94.5 ft·lb, which is precisely what the Xero displayed for that shot. Same number, to the decimal.

If you've wondered about the Xero's "power factor" column: it's momentum wearing different units — weight × speed ÷ 1,000, in kilograin-feet per second. ArrowForge reports momentum in slug·ft/s (the unit the game-class penetration thresholds use); multiply by 225.4 and you get the Garmin number. The app's momentum popup now shows the Garmin-style power factor alongside, so you can cross-check your chrono screen directly.

Honest limitations

Still one bow, one draw weight, and arrows spanning 455–548 grains. The 0.93 energy efficiency and the 0.024 ft·lb-per-grain slope are fit to this bow; other cam systems will land somewhat differently. The draw-weight term (2 fps per pound) remains the industry rule of thumb — isolating it cleanly still needs chrono sessions at a second poundage, and that's still on the list. And arrows lighter than ~450 grains are extrapolation: the curve now bends the way physics says it should, but I haven't shot it yet.

That's the pattern of this whole series, though: shoot, measure, find where the formula disagrees with the chronograph, and let the data decide. Three posts in, the estimate has gone from −5.5 fps on a good day to ±0.9 across everything I can throw at it.