The Royal Clipper (Figure 10.1) has a total sail area of $$5200 \mathrm {~m} ^ { 2 } \text {. Show that }$$ the estimate for the total power of a large sailing ship as given in the text is reasonable.

Question

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The Answer is The total power available is

P = \left( 0.602 \mathrm {~kg} / \mathrm { m } ^ { 3 } ight) imes A v ^ { 3 }

so the velocity is

v = \left[ \frac { P } { \left( 0.602 \mathrm {~kg} / \mathrm { m } ^ { 3 } ight) A } ight] ^ { 1 / 3 }

Using the estimated power,

8 \mathrm { MW }

, and the given sail area,

5200 \mathrm {~m} ^ { 2 }

, then

v = \left[ \frac { 8 imes 10 ^ { 6 } \mathrm {~W} } { \left( 0.602 \mathrm {~kg} / \mathrm { m } ^ { 3 } ight) imes \left( 5200 \mathrm {~m} ^ { 2 } ight. } ight] ^ { 1 / 3 } = 13.6 \mathrm {~m} / \mathrm { s }

This is a reasonable value for a strong wind

The Royal Clipper (Figure 10 5200 m2. Show that 5200 \mathrm {~m} ^ { 2 } \text {. Show that }5200 m2. Show that

The Royal Clipper (Figure 10 $5200 \mathrm {~m} ^ { 2 } \text {. Show that }$