A sail responds to the apparent wind, the vector sum of the true wind and the wind created by the boat’s own motion, so the same 5 m/s true wind gives an apparent wind of 6.57 m/s when a 2 m/s boat is close-hauled, 5.39 m/s on a beam reach and only 3.0 m/s running, which means the dynamic pressure on the sail is 4.8 times higher close-hauled than running. Running therefore feels calm because the boat’s speed cancels part of the wind, and turning up from a run into a reach multiplies the force on the sail by about 3.2 before any gust arrives.
Part of Small Sailboat Construction
Points of sail are the headings a boat can take relative to the true wind direction, from close-hauled, nearest the wind, through reaching to running with the wind behind.
The Sail Feels A Different Wind From The One On Your Face
On shore you feel the true wind. Once the boat moves, it carries its own headwind: a boat travelling at speed V_b meets still air as if the wind were blowing at V_b from dead ahead. The sail experiences the sum of the two. The carrier’s classification (close-hauled about 45° off the wind and slowest; reaching fastest; running risky because it feels calm) comes straight out of that sum, and with a little trigonometry it can be computed rather than remembered.
Let the true wind speed be V_t, arriving at an angle β measured from the bow (β = 0° is dead ahead; β = 180° is dead astern), and the boat speed V_b along its heading. Along the boat’s axis, the apparent wind has the component V_t cos β + V_b; across the boat it has V_t sin β. Then
- apparent speed V_a = √[(V_t cos β + V_b)² + (V_t sin β)²]
- apparent angle α = arctan[V_t sin β ÷ (V_t cos β + V_b)], with the quadrant taken from the signs.
What You Need
- A calculator with sine and cosine, or a drawing: draw V_t as an arrow, add V_b, measure the sum
- A boat speed estimate (see Basic Sailing Skills for a way to time yourself over a measured distance)
- A wind estimate from Wind Speed Estimation: 5 m/s is 18 km/h, inside force 3
Method: Compute The Apparent Wind
Step 1: Choose V_t and V_b. Here V_t = 5 m/s and V_b = 2 m/s, held at 2 m/s on every heading for clarity. A real boat’s speed varies with heading, so use your own measured values.
Step 2: Compute the two components for each β.
Step 3: Convert to V_a and α and to dynamic pressure q = ½ × 1.225 × V_a².
Step 4: Compare each q with the running value.
Worked Example: Four Headings, One Wind
| True wind angle β | Along-boat V_t cos β + V_b | Across V_t sin β | Apparent speed | Apparent angle | q (N/m²) | q ÷ running |
|---|---|---|---|---|---|---|
| 45° (close-hauled) | 5 × 0.707 + 2 = 5.54 | 3.54 | 6.57 m/s | 32.6° | 26.4 | 4.79 |
| 90° (beam reach) | 0 + 2 = 2.00 | 5.00 | 5.39 m/s | 68.2° | 17.8 | 3.22 |
| 135° (broad reach) | 5 × (−0.707) + 2 = −1.54 | 3.54 | 3.85 m/s | 113.5° | 9.1 | 1.65 |
| 180° (running) | −5 + 2 = −3.00 | 0 | 3.00 m/s | astern | 5.5 | 1.00 |
Three conclusions follow, and the first two need no coefficient.
- Bearing away looks gentler than it is. Going from close-hauled to running cuts the wind on the sail from 6.57 to 3.0 m/s. Going back, the pressure rises 4.79 times. The calm feeling downwind is a vector effect, and it ends the moment the helm goes up.
- The sail is trimmed to the apparent angle, not the true one. Close-hauled at 45° to the true wind the sail sees the wind at 32.6° from the bow, so sheeting for 45° leaves the sail too far out.
- Pointing has a price in speed made good. At 3 m/s, a boat that holds 45° makes 3 cos 45° = 2.12 m/s upwind; one that holds 60° makes 1.50 m/s. Leeway adds to the angle actually sailed, so the board matters (see Centerboard or Leeboard).
This analysis uses no empirical coefficient except the air density; it does not say how close to the wind any given home-made sail can point, which must be measured with your own boat.
Common Mistakes
- Trimming to the true wind — use a telltale (a strip of cloth on the shroud) to read the apparent wind.
- Assuming a gust feels the same on every heading — a 3 m/s increase in true wind raises the running apparent wind from 3.0 to 6.0 m/s.
- Forgetting that boat speed is not constant — as the boat accelerates the apparent wind moves toward the bow.
Safety
The lull downwind is a trap
A boat running before a wind of force 3 can have an apparent wind of 3 m/s; turning up to a beam reach in the same wind raises the dynamic pressure to 17.8 N/m², 3.2 times as much, and to 26.4 N/m², 4.8 times, if it turns on to close-hauled. Ease the sheet before you turn up, not after, and keep the crew weight low and to windward. See Safety & Capsizing Recovery.
What’s Next
- Learn next: Tacking & Jibing — passing through the wind
- Combine with: Spritsail Rig — what the dynamic pressure does to a real sail