Question 4.5: Convert (a) 450 knots into kph and (b) 120 m/s into mph.
Convert (a) 450 knots into kph and (b) 120 m/s into mph.
We could simply multiply by the relevant conversion factors in Table 4.7, which for (a) is the reciprocal of 0.5400 or 1.852. Similarly, for (b), the conversion factor is 2.23694. But let us see if we can derive these conversion factors by addressing the problem in a rather circular manner.
| Quantity | SI unit | Conversion factor→ | Imperial/other recognized units |
| Acceleration | metre/second² (m/s²) | 3.28084 | feet/second² (ft/s²) |
| Angular measure | radian (rad) | 57.296 | degrees (°) |
| radian/second (rad/s) | 9.5493 | revolutions per minute (rpm) |
|
| Area | metre² (m²) | 10.7639 | feet² (ft²) |
| metre² (m²) | 6.4516 × 10^4 | inch² (in²) | |
| Density | kilogram/metre³ (kg/m³) | 0.062428 | pound/foot³ (lb/ft³) |
| kilogram/metre³ (kg/m³) | 3.6127 × 10^{-5} | pound/inch³ (lb/in³) | |
| kilogram/metre³ (kg/m³) | 0.010022 | pound/gallon (UK) | |
| Energy, work, heat | joule (J) | 0.7376 | foot pound-force (ft lbf) |
| joule (J) | 9.4783 × 10^{-4} | British thermal unit (btu) | |
| joule (J) | 0.2388 | calorie (cal) | |
| Flow rate | m³ /s (Q) | 35.315 | ft³ /s |
| m³ /s (Q) | 13,200 | gal/min (UK) | |
| Force | Newton (N) | 0.2248 | pound-force (lbf) |
| Newton (N) | 7.233 | poundal | |
| kilo-Newton | 0.1004 | ton-force (UK) | |
| Heat transfer | watt (W) | 3.412 | btu/h |
| watt (W) | 0.8598 | kcal/h | |
| watt/metre² kelvin (W/m² K) | 0.1761 | btu/h ft² °F | |
| Illumination | lux (lx) | 0.0929 | foot candle |
| lux (lx) | 0.0929 | lumen/foot² (lm/ft²) | |
| candela/metre² (cd/m²) | 0.0929 | candela/ft² (cd/ft²) | |
| Length | metre (m) | 1 × 1010 | angstrom |
| metre (m) | 39.37008 | inch (in) | |
| metre (m) | 3.28084 | feet (ft) | |
| metre (m) | 1.09361 | yard (yd) | |
| kilometre (km) | 0.621371 | mile | |
| kilometre (km) | 0.54 | nautical miles | |
| Mass | kilogram (kg) | 2.20462 | pound (lb) |
| kilogram (kg) | 35.27392 | ounce (oz) | |
| kilogram (kg) | 35.27392 | slug | |
| tonne (t) | 0.984207 | ton (UK) | |
| tonne (t) | 1.10231 | ton (US) | |
| Moment, torque | Newton-metre (Nm) | 0.73756 | foot pound-force (ft lbf) |
| Newton-metre (Nm) | 8.8507 | inch pound-force (in. lbf) | |
| Moment of inertia (mass) | kilogram-metre squared (kgm²) | 0.7376 | slug-foot squared (slug ft²) |
| Second moment of area | millimeters to the fourth (mm^4) | 2.4 × 10^{-6} | inch to the fourth (in^4) |
| Power | watt (W) | 3.4121 | British thermal unit/hour (btu/h) |
| watt (W) | 0.73756 | foot pound-force/second (ft lbf/s) |
|
| kilowatt (kW) | 1.341 | horsepower | |
| horsepower (hp) | 550 | foot pound-force/second (ft.lbf/s) |
|
| Pressure, stress | kilopascal (kPa) | 0.009869 | atmosphere (atm) |
| kilopascal (kPa) | 0.145 | pound-force/inch² (psi) | |
| kilopascal (kPa) | 0.01 | bar | |
| kilopascal (kPa) | 0.2953 | inches of mercury | |
| pascal | 1.0 | Newton/metre² (N/m²) | |
| megapascal (MPa) | 145.0 | pound-force/inch² (psi) | |
| Temperature | kelvin (K) | 1.0 | celsius (C) |
| kelvin (K) | 1.8 | rankine (R) | |
| kelvin (K) | 1.8 | fahrenheit (F) | |
| kelvin (K) | °C + 273.15 | ||
| kelvin (K) | (°F + 459.67)/1.8 | ||
| celsius (°C) | (°F – 32)/1.8 | ||
| Velocity | metre/second (m/s) | 3.28084 | feet/second (ft/s) |
| metre/second (m/s) | 196.85 | feet/minute (ft/min) | |
| metre/second (m/s) | 2.23694 | miles/hour (mph) | |
| kilometre/hour (kph) | 0.621371 | miles/hour (mph) | |
| kilometre/hour (kph) | 0.5400 | knot (international) | |
| Viscosity (kinematic) | square metre/second (m² /s) |
1 × 10^{6} | centi-stoke |
| square metre/second (m² /s) |
1 × 10^{4} | stoke | |
| square metre/second (m² /s) |
10.764 | square feet/second (ft² /s) |
|
| Viscosity (dynamic) | pascal second (Pa s) | 1000 | centipoise (cP) |
| centipoise (cP) | 2.419 | pound/feet hour (lb/ft h) | |
| Volume | cubic metre (m³) | 35.315 | cubic feet (ft³) |
| cubic metre (m³) | 1.308 | cubic yard (yd³) | |
| cubic metre (m³) | 1000 | litre (l) | |
| litre (l) | 1.76 | pint (pt) UK | |
| litre (l) | 0.22 | gallon (gal) UK |
a) Suppose we know that there are 6080 ft in a knot. Then, since there are 3.28084 ft in 1 m, there are \frac{6080}{3.28084} = 1853.18 m in a knot.
Therefore, 450 knots = 450 × 1853.18 m/h or 833.93 kph.
Thus, to convert knots to kph, we need to multiply them by \frac{833.93}{450} = 1.853, which to two decimal places agrees with our tabulated value.
b) A conversion factor to convert m/s into mph may be found in a similar manner. In this case we start with the fact that 1 m = 3.28084 ft and there are 5280 ft in a mile, so:
120 m/s = 3.28.04 × 120 feet per second
or
\frac{3.28084 \times 120}{5280} miles per second
We also know that there are 3600 s in an hour. Therefore:
\begin{aligned}120 \ m / s &=\frac{3.28084} \times 120 \times {3600}{5280} \\&=268.4 \ mph\end{aligned}
Again the multiplying factor is given by the ratio 268.4/120 = 2.2369, which is in agreement with our tabulated value.