where substitutions for 7, P, Q, and p? 62 were made from Equations [12], [9], [10], and [4]. 
This is exactly the result obtained by Dryden and Kuethe® using the assumption that there 
were no temperature gradients in the wire. 
The dimensionless time constants yM,/b? and y M,/b? are plotted against P/x, in 
Figures 3 and 4 and against P/x, in Figure 5. Figures 3 and 4 show the effects of the coat- 
ing thickness and Figure 5 shows the effect of the heat conductivity of the coating. 
In Figure 6 typical curves are drawn for the step responses of a constant-current coated 
wire to a change in current and to a change in convective cooling as functions of t¢/M,. On 
the same graph the response of a bare wire with time constant M, is represented by the dotted 
line. It is clear that the step response to a change in current input is very close to a simple 
exponential function. As the coating thickness decreases and its heat conductivity increases, 
the step response of the coated wire to a change in convective cooling also approaches the 
exponential curve. 
The frequency responses corresponding to these step responses are shown in Figure 7 
as functions of aM). When w = 1/M, the amplitude of the bare-wire response is reduced to 
0.707. The frequency response of the coated wire to a change in current is very nearly the 
same as the bare-wire response but the frequency response to a change in convective cooling 
is lower for all frequencies. The ordinate of the latter curve is approximately 0.707 when 
o=1/M,. 
It is common practice to design a compensating circuit which will correct the distortion 
in the bare-wire response. The elements of this circuit may be adjusted by assuring a satis- 
factory frequency response to a current input since the two time constants are nearly identical. 
As the response of a constant-current coated wire to a step-like change in convective cooling 
is not a simple exponential function a different type of electronic circuit would be needed to 
fully correct the distortion in the response. If the coating is thin, or if Q/x, is only slightly 
smaller than P/x,, the two time constants are nearly equal and the response of the wire to a 
step-like change in convective cooling is well approximated by a simple exponential function. 
In this case the bare-wire compensating circuit can be used in the conventional manner to 
correct the distortion in the wire response. The effectiveness of the compensation decreases 
as the coating thickness increases and as the difference between P and Q increases. 
In hot-wire anemometry the hot-wire element is usually given a particular temperature 
increase over the ambient temperature of the flow. This temperature increment is measured 
in terms of an overheating ratio a, defined as 
Teale ieee Ae 
Wh ey ee ee [120] 
Tie Ty ate a e 
where 
B28, Dl eaGr, =m) [121] 
24 
