You could try working out the next level of approximation using A level physics, but I suspect you'd fail as you wouldn't be able to work out the temperature gradient without additional information.
The pressure gradient is given by the hydrostatic equation: [
dP/dh = -rho * g] where P = Pressure, h = geopotential altitude, rho = density, g = gravitational force.
g is constant at 9.80665 m/s^2 (ISA value)
Density as a function of pressure in the atmosphere can be obtained from [
rho = P/R*T] where R = 287.1J/Kg/K (specific gas constant for dry air, ISA value) and T = temperature in Kelvin, obtainable as a function of lapse rate L and height [
T = T0 - L * h]
So for example:
1) ISA change of height per mb at MSL:
dh/dP = (-1.225Kg/m^3 * 9.80665m/s^2)^-1
= -0.0832421398m/Pa
= -27.3104133ft/mb
2) ISA change of height per mb at the 300mb pressure level (30065ft=9163.8m[*] geopotential altitude)
T = 288.15K-0.0065K/m*9163.8m = 228.6K
rho = 30000Pa / (287.1 J/Kg/K * 228.6K)
= 0.457100647Kg/m^3
dh/dP = (-0.457100647Kg/m^3 * 9.80665m/s^2)^-1
= -0.22308352m/Pa
= -73.1901312ft/mb
[*] The geopotential altitude in metres for a given tropospheric pressure level in Pa can be obtained by the formula [
(1.0 - (P/101325)^0.190263))*(288.15/0.0065)] which is derived by pulling one's hair while rearranging various ISA equations, or from an ISA tabulation.
All very simple stuff really
(unless one goes and asks the gurus over at Tech Log) 