Chapter 14, Problem 19P

To determine

Create a table that shows the windchill temperatures for the given range of ambient air temperature and wind speed.

Answer to Problem 19P

A table is created for the windchill temperatures with the given range of ambient air temperature and wind speed by using excel.

Explanation of Solution

Given data:

The range of ambient air temperature is $-30°\text{C}<T_a<10°\text{C}$.

The range of wind speed is $20\frac{\text{km}}{\text{h}}<V<80\frac{\text{km}}{\text{h}}$

Formula used:

Formula to calculate the more common equivalent windchill temperatures is,

$T_{\text{equivalent}}=0.045\left(5.27V^{0.5}+10.45-0.28V\right)\left(T_a-33\right)+33$

Here,

$T_a$ is the ambient air temperature in $°\text{C}$, and

$V$ is the wind speed in $\frac{\text{km}}{\text{h}}$.

Calculation:

Refer to the Figure 1:

Column A shows the wind speed (V) with range from $20\frac{\text{km}}{\text{h}}<V<80\frac{\text{km}}{\text{h}}$ in increment of 10 and Row 8 shows the ambient air temperature with range from $-30°\text{C}<T_a<10°\text{C}$ in increment of 5.

For the cell B9, the formula used to find the equivalent windchill temperatures as “$=0.045\left(5.27V^{0.5}+10.45-0.28V\right)\left(T_a-33\right)+33$”.

Written as “=(0.045*((5.27*($A$9)^0.5)+10.45-(0.28*$A$9))*(B8-33))+33”. Here, B8 cell represents the value of ambient air temperature is $-30$ and $\text{\$A\$9}$ is an absolute cell reference which represent the value of cell A9 as $20$. The result obtained in the cell B9 would be $-47.6$. Use the Fill command to copy the formula into cell C9, only the B8 cell in the formula is automatically substituted by C8, resulting in a value $-41.2$. Then, by click and drag the bottom corner of the C9 cell extend through J9 in row-wise. The result is obtained as in Table 1.

For the cell B10, the formula used to find the equivalent windchill temperatures as “$=0.045\left(5.27V^{0.5}+10.45-0.28V\right)\left(T_a-33\right)+33$”.

Written as “=(0.045*((5.27*($A$10)^0.5)+10.45-(0.28*$A$10))*(B8-33))+33”. Here, B8 cell represents the value of ambient air temperature is $-30$ and $\text{\$A\$10}$ is an absolute cell reference which represent the value of cell A10 as $30$. The result obtained in the cell B10 would be $-54.6$. Use the Fill command to copy the formula into cell C10, only the B8 cell in the formula is automatically substituted by C8, resulting in a value $-47.7$. Then, by click and drag the bottom corner of the C10 cell extend through J10 in row-wise. The result is obtained as in Table 1.

For the cell B11, the formula used to find the equivalent windchill temperatures as “$=0.045\left(5.27V^{0.5}+10.45-0.28V\right)\left(T_a-33\right)+33$”.

Written as “=(0.045*((5.27*($A$11)^0.5)+10.45-(0.28*$A$11))*(B8-33))+33”. Here, B8 cell represents the value of ambient air temperature is $-30$ and $\text{\$A\$11}$ is an absolute cell reference which represent the value of cell A11 as $40$. The result obtained in the cell B11 would be $-59.4$. Use the Fill command to copy the formula into cell C11, only the B8 cell in the formula is automatically substituted by C8, resulting in a value $-52.0$. Then, by click and drag the bottom corner of the C11 cell extend through J11 in row-wise. The result is obtained as in Table 1.

For the cell B12, the formula used to find the equivalent windchill temperatures as “$=0.045\left(5.27V^{0.5}+10.45-0.28V\right)\left(T_a-33\right)+33$”.

Written as “=(0.045*((5.27*($A$12)^0.5)+10.45-(0.28*$A$12))*(B8-33))+33”. Here, B8 cell represents the value of ambient air temperature is $-30$ and $\text{\$A\$12}$ is an absolute cell reference which represent the value of cell A12 as $50$. The result obtained in the cell B12 would be $-62.6$. Use the Fill command to copy the formula into cell C12, only the B8 cell in the formula is automatically substituted by C8, resulting in a value $-55.0$. Then, by click and drag the bottom corner of the C12 cell extend through J12 in row-wise. The result is obtained as in Table 1.

For the cell B13, the formula used to find the equivalent windchill temperatures as “$=0.045\left(5.27V^{0.5}+10.45-0.28V\right)\left(T_a-33\right)+33$”.

Written as “=(0.045*((5.27*($A$13)^0.5)+10.45-(0.28*$A$13))*(B8-33))+33”. Here, B8 cell represents the value of ambient air temperature is $-30$ and $\text{\$A\$13}$ is an absolute cell reference which represent the value of cell A13 as $60$. The result obtained in the cell B13 would be $-64.7$. Use the Fill command to copy the formula into cell C13, only the B8 cell in the formula is automatically substituted by C8, resulting in a value $-57.0$. Then, by click and drag the bottom corner of the C13 cell extend through J13 in row-wise. The result is obtained as in Table 1.

For the cell B14, the formula used to find the equivalent windchill temperatures as “$=0.045\left(5.27V^{0.5}+10.45-0.28V\right)\left(T_a-33\right)+33$”.

Written as “=(0.045*((5.27*($A$14)^0.5)+10.45-(0.28*$A$14))*(B8-33))+33”. Here, B8 cell represents the value of ambient air temperature is $-30$ and $\text{\$A\$14}$ is an absolute cell reference which represent the value of cell A14 as $70$. The result obtained in the cell B14 would be $-66.1$. Use the Fill command to copy the formula into cell C14, only the B8 cell in the formula is automatically substituted by C8, resulting in a value $-58.2$. Then, by click and drag the bottom corner of the C14 cell extend through J14 in row-wise. The result is obtained as in Table 1.

For the cell B15, the formula used to find the equivalent windchill temperatures as “$=0.045\left(5.27V^{0.5}+10.45-0.28V\right)\left(T_a-33\right)+33$”.

Written as “=(0.045*((5.27*($A$15)^0.5)+10.45-(0.28*$A$15))*(B8-33))+33”. Here, B8 cell represents the value of ambient air temperature is $-30$ and $\text{\$A\$15}$ is an absolute cell reference which represent the value of cell A15 as $80$. The result obtained in the cell B15 would be $-66.8$. Use the Fill command to copy the formula into cell C15, only the B8 cell in the formula is automatically substituted by C8, resulting in a value $-58.8$. Then, by click and drag the bottom corner of the C15 cell extend through J15 in row-wise. The result is obtained as in Table 1.

Table 1 is created to shows a Wind Chill Temperature.

Table 1

Wind speed (Km/h)	Ambient Temperature $\left(°\text{C}\right)$
	-30	-25	-20	-15	-10	-5	0	5	10
20	-47.6	-41.2	-34.8	-28.4	-22.0	-15.6	-9.2	-2.8	3.6
30	-54.6	-47.7	-40.7	-33.8	-26.8	-19.9	-12.9	-6.0	1.0
40	-59.4	-52.0	-44.7	-37.4	-30.0	-22.7	-15.4	-8.1	-0.7
50	-62.6	-55.0	-47.4	-39.8	-32.2	-24.7	-17.1	-9.5	-1.9
60	-64.7	-57.0	-49.2	-41.5	-33.7	-25.9	-18.2	-10.4	-2.7
70	-66.1	-58.2	-50.3	-42.5	-34.6	-26.8	-18.9	-11.0	-3.2
80	-66.8	-58.8	-50.9	-43.0	-35.1	-27.2	-19.3	-11.3	-3.4

Figure 2 shows a wind chill table in the excel sheet has obtained as similar to given Problem 14.19 in the textbook

Conclusion:

Hence, a table is created for the windchill temperatures with the given range of an ambient air temperature, and wind speed have been explained using excel.