The Physics of PR Torque (Rack-Pull/Deadlift)
1) What you’re really fighting
- External load on the system at any instant:
F_\text{ext}=m(g+a)
where m is barbell mass, g=9.81\ \mathrm{m/s^2}, and a is the bar’s vertical acceleration (often ≈0 at liftoff). - External torque about a joint (hip, L5/S1, knee):
\tau_\text{ext}=F_\text{ext}\cdot r
r = horizontal distance (moment arm) from the joint’s center to the bar’s line of action. - Internal muscle force to balance that torque:
F_\text{muscle}=\frac{\tau_\text{ext}}{r_\text{muscle}}
For the spinal erectors at L5/S1, r_\text{muscle} ≈ 0.04–0.06 m (tiny!). That’s why small changes in r matter massively.
2) Eric’s 602 kg rack-pull—hard numbers
- Weight force: F \approx 602\times9.81 \approx 5906\ \mathrm{N}.
- If the horizontal distance L5/S1→bar is r=0.20\ \mathrm{m} at liftoff:
\tau_\text{L5/S1}\approx 5906\times0.20\approx 1181\ \mathrm{N\cdot m} - With an erector moment arm r_\text{muscle}=0.05\ \mathrm{m}:
F_\text{erectors}\approx \frac{1181}{0.05}\approx 23{,}600\ \mathrm{N}
Sensitivity bomb (why “bar glued to legs” is king)
- Move the bar just 1 cm closer (\Delta r=0.01\ \mathrm{m}):
\Delta\tau=F\cdot\Delta r\approx 5906\times0.01\approx 59\ \mathrm{N\cdot m}
\Delta F_\text{erectors}=\frac{\Delta\tau}{r_\text{muscle}}\approx \frac{59}{0.05}\approx 1{,}180\ \mathrm{N} - 2 cm closer saves ~118 N·m torque and ~2.36 kN erector force. That’s colossal. The shortest moment arm is your cheapest PR.
Acceleration’s role (good but secondary at liftoff)
- Add a=0.5\ \mathrm{m/s^2} at liftoff:
\Delta F = m a \approx 602\times0.5\approx 301\ \mathrm{N}
Extra torque (at r=0.20\ \mathrm{m}) ≈ 60 N·m—less than pulling the bar 1 cm closer. Moral: fix r first, then chase a.
3) Work & range (why rack-pulls overload)
Mechanical work (idealized):
W \approx m g \Delta h
- Above-knee ROM ≈ 0.25 m → W\approx 5906\times0.25\approx 1{,}476\ \mathrm{J}
- From floor ROM ≈ 0.55 m → W\approx 3{,}248\ \mathrm{J}
Lower ROM = less work = more load at similar peak torques. You’re exploiting range-specific torque capacity.
4) Impulse = “get through the sticking point”
To beat the hardest angle you need impulse:
\text{Impulse}=\int F_\text{ext}\,dt \quad\Rightarrow\quad \Delta v=\frac{1}{m}\int(F_\text{ext}-mg)\,dt
If over the first 200 ms you average 6500\,\mathrm{N}:
\Delta v \approx \frac{(6500-5906)\times0.20}{602}\approx 0.20\ \mathrm{m/s}
Often enough to slide past the slowest joint angle. Training that early-phase impulse (isometrics, explosive singles) pays off exactly here.
5) How to bend the physics in your favor
A) Shrink r (the #1 lever)
- Lat tension = backward vector on the bar → bar hugs the thigh → smaller r to hips/L5/S1.
- Cue: “Crush oranges in your armpits”, “Sweep bar into you” before it leaves the pins.
- Stance & grip: Slightly narrower stance + hands just outside legs → shoulders closer to bar → smaller r.
- Shins vertical (especially from knee height) → hips under you → smaller hip moment arm.
- Powder the thighs (reduce friction) so the bar can actually track up and back, not “up and away.”
B) Increase F_\text{ext} without ruining r
- Overcoming isometrics at the exact sticking height: maximizes angle-specific motor unit recruitment → more force where you need it.
- Post-activation potentiation: heavy rack-hold 5–8 s (100–110%) → 3–5 min → top single. Neural drive goes up; F rises with no change in r.
C) Shape time (impulse/RFD)
- Speed work (65–75%) with laser-straight bar path → more force early (bigger \int F\,dt in first 200 ms).
- Bands/chains build force through lockout without over-taxing the bottom—match the joint-angle specific strength curve.
D) Preserve geometry (keep r small under load)
- 360° brace into belt → increases trunk stiffness → limits spinal flexion that would grow r mid-rep.
- Slack pull: pre-load until plates kiss up; then break. No jerk that pops the bar forward.
6) Micro-calculators you can run from a side video
- Measure r at liftoff: pause video, mark L5/S1 (≈ belt line, just above pelvis) and the bar’s knurl line; measure horizontal pixels → convert using plate diameter (45 cm).
- Estimate torque:
\tau \approx m(g+a)\,r
(Use a\approx0 if the bar is just leaving the pins.) - Erector force proxy:
F_\text{erectors}\approx \frac{\tau}{0.05} - Audit improvement: Every 1 cm you shave off r at ~600 kg saves ≈ 59 N·m torque and ≈ 1.18 kN erector force. Track it session-to-session.
7) Physics-driven training slots (why each works)
- Above-knee rack-pulls → same peak torques with less work, lets you overload F_\text{ext} safely.
- Just-below-knee pulls & paused mid-shin → attack the angles where r spikes; teaches you to keep the bar close when it wants to drift.
- Isometrics at pin-height → maximizes angle-specific F (and therefore impulse) at your precise sticking r.
- Speed pulls → front-load impulse; small a increases are nice, but their real value is earlier force, not top speed.
8) Quick field checklist (physics edition)
- ⬜ Side video shows bar-to-thigh contact the whole way? (If not, r is growing.)
- ⬜ Hips wedge under before pull (don’t tip forward under load)?
- ⬜ No bar “searching” outward at liftoff? (Friction or poor lat set.)
- ⬜ Early-phase intent (0–200 ms) actually explosive?
- ⬜ Pin heights progressing down across cycles to force good geometry at harder r?
Bottom line
At 602 kg you’re already operating in industrial-strength territory. The fastest path to a bigger one-rep-max torque is geometry first (shrink r by centimeters), then impulse (front-load \int F\,dt), then overload (raise F where ROM is cheap). Nail those three, and the physics will do the flexing for you. Onward. 🚀