Maps for Math

Why should a hammock hang at 30 degrees?

Your weight and the two strap pulls are force arrows that must add to zero. Only the upward part of each strap holds you, and at 30° that part is exactly half the strap's pull, so each strap carries your full weight. Hang it flat at 10° and each strap pulls almost three times your weight.

490 lb at 15°546 lb at 30°load 400 lb (2 × your weight)The arrows add to zerostrap + strap + weightbiggest pull: 2.73 × weight
Left strap tension
490 lbf
Right strap tension
546 lbf
Sideways pull on each tree
473 lbf
Biggest strap pull ÷ your weight
×2.73

Bouncing and dropping in spike the load for a moment. Check that your straps, hardware, and trees are rated well above these numbers.

Challenge: Hold 250 lb or more with neither strap pulling more than your weight, and one strap at 35° or less.

×
Flopping in, bouncing, or swinging spikes the load for a moment. Dropping in hard can briefly double it or more.

Play

Start with the 30° rule, then flatten the straps and watch the pull grow. Try the lopsided hang.

Challenge: Hold 250 lb or more with neither strap pulling more than your weight, and one strap at 35° or less. The box under the picture turns green when you get it.

Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”

Understand

T1=Wcos⁡θ2sin⁡(θ1+θ2),T2=Wcos⁡θ1sin⁡(θ1+θ2)T_1 = \frac{W\cos\theta_2}{\sin(\theta_1 + \theta_2)},\quad T_2 = \frac{W\cos\theta_1}{\sin(\theta_1 + \theta_2)}

The hammock isn't moving, so the three forces on it, two strap pulls and your weight, must add up to zero. As arrows placed tip to tail, they close into a triangle.

Split each strap's pull into sideways and upward parts. The sideways parts cancel, and the upward parts must add up to your weight:

T1sin⁡θ1+T2sin⁡θ2=WT_1\sin\theta_1 + T_2\sin\theta_2 = W

At 30°, sin⁡30°=12\sin 30° = \tfrac{1}{2}, so each strap pulls exactly your weight.

Use

Every input has a unit menu, so you can type values in the units you already have. Results follow your units.

Show the work

  1. Nothing is moving, so the three force arrows add to zero\vec T_1 + \vec T_2 + \vec W = \vec 0
  2. Sideways parts cancelT_1\cos\theta_1 = T_2\cos\theta_2
  3. Upward parts hold the weightT_1\sin\theta_1 + T_2\sin\theta_2 = W
  4. Solve the two equationsT_1 = \frac{400\cos 30^\circ}{\sin(15^\circ + 30^\circ)} = 489.9\ \text{lb}
  5. And the other strapT_2 = \frac{400\cos 15^\circ}{\sin(15^\circ + 30^\circ)} = 546.4\ \text{lb}
  6. Same angle on both sides simplifies toT = \frac{W}{2\sin\theta}\quad (30^\circ:\ \tfrac{W}{2 \times 0.5} = W)

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Set each strap's angle above level and the weight.

  • The dynamic factor covers bouncing, swinging, or dropping in, which spike the load for a moment. Dropping in hard can briefly double it or more.

For learning and estimation. Verify with applicable codes, standards, and a qualified professional before using in design, construction, or safety-critical work.

Cheat card

T⃗1+T⃗2+W⃗=0⃗\vec T_1 + \vec T_2 + \vec W = \vec 0
T=W2sin⁡θ (both straps at θ)T = \frac{W}{2\sin\theta}\ \text{(both straps at } \theta\text{)}
T1=Wcos⁡θ2sin⁡(θ1+θ2)T_1 = \frac{W\cos\theta_2}{\sin(\theta_1 + \theta_2)}
SymbolMeaningUnit
WWweight in the hammocklb
T1,T2T_1, T_2strap tensionslb
θ\thetastrap angle above level°
  • At 30°, each strap pulls your full weight. Flatter means more.
  • In a lopsided hang, the steeper strap carries more.
  • The sideways pull on the trees is the same on both sides.

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Where it’s used

  • Physics
    Any hanging object, from a traffic light to a bridge cable, balances force vectors this way.
  • Civil & Construction
    Engineers size cables and anchors from these tensions, with a big safety margin.
  • Hobbies & Crafts
    Set up a hammock or a slackline without overloading the straps or the trees.

Questions people ask

Why does a tight hammock pull so hard?

Only the upward part of each strap holds you up. A nearly flat strap has a tiny upward part, so the whole pull has to be huge to add up to your weight.

Which strap works harder in a lopsided hang?

The steeper one. The sideways pulls must cancel, and a steep strap needs more total pull to match the flatter strap's sideways part.

Does this apply to clotheslines and slacklines?

Yes. A small sag in the middle means very high tension at the ends, which is why tight lines need strong anchors.

Sample VEC-0004 · rev 1 · model VEC-M04 · Level 3 · algebra · updated 2026-09-29