The Lemurian approximation is a substantial improvement over the "2 per cent per thousand feet" variant. Finding a good approximation suitable over all altitudes, speeds and temperature deviations of interest (MSL to tropopause, 100 to 300 kcas, +/- 30 K) for TAS without using quadratic terms is next to impossible. Having looked at a restricted range of altitudes (MSL to 10 000 feet) it is hard to improve on Lemurian's approximation. The only value I would alter is the constant 600, which I propose be swapped for 666.67 (i.e. 3/2000). This is mentally no more difficult than dividing the altitude by 600 but the error is lower.
Here are three charts comparing the errors in KTAS across the restricted altitude range for these three approximations.
Approximation (a): TAS ≈ CAS[1+(2/100)(h_DA/1000)]
Approximation (b): TAS ≈ CAS{1+(1/100)[(h_PA/600)+(T_dev/5)]}
Approximation (c): TAS ≈ CAS{1+(1/100)[(3h_PA/2000)+(T_dev/5)]}
T_dev is temperature deviation from the standard atmosphere.
h_PA is the pressure altitude in feet.
h_DA is the density altitude in feet.
Note: Pressure altitude is used in approximations (b) and (c), but density altitude in approximation (a).
In the altitude range 0 to 10 000 feet the least square error for all CAS (100 to 300 kcas) and temperature deviation (+/- 30 K) pairs is lowest under approximation (c). The curves are plotted for Tdev=0 therefore no density altitude axis is included for charts 1 and 2. Send PM for excel file.
Chart 1: comparison of approximations (a) and (b).
Chart 2: comparison of approximations (a) and (c).
Chart 3: comparison of approximations (b) and (c).