W. STEPHEN WOODWARD
Venable Hall, CB3290, University of North Carolina, Chapel Hill, NC 27599-
3290; Internet: woodward@net.chem.unc.edu.
ELECTRONIC DESIGN / JUNE 9, 1997から引用
A
mong the many methods used
for measuring air speed, one approach excels in applications related to aerodynamics and wind
power: the Pitot-tube impact-pressure air-speed indicator. The so-called
“impact” or “stagnation” pressure exerted by airflow striking a surface is
given by P = (D × V2)/2, where D = air
density and V is air speed. Pitot tube
anemometry uses this relationship to
produce: V = √( 2P/D).
Although it might seem that this
dependence of the air-speed estimate
upon density is an undesirable complication, it’s actually advantageous in
those applications to which Pitot-tube
anemometers are uniquely suited.
This is true because, in these applications, the forces of primary interest
(e.g., lift from an airplane’s wing or
propulsion from a boat’s sail) are
themselves related directly to impact
pressure and therefore to air density.
The air speed measured by a Pitot
tube is automatically compensated for
variations in air density caused by
changes in temperature, barometric
pressure, or altitude. It’s therefore exactly the air-speed information most
wanted by the pilot or sailor.
The heart of the Pitot tube airspeed indicator is piezoresistive differential pressure sensor G1. Op amp
A1, in combination with VR1 and R1,
R2, and R3 controls Q1 and Q2 to generate constant-current-bridge bias I1
= 500 µA. In response, G1 produces a
differential voltage (V1 - V2) equal, after zero compensation via R4, R5, R6,
and R7 to approximately 8 mV/psig of
impact pressure. The A2, A3 differential pair controls Q3 so as to convert
(V1 - V2) to impact-pressure-proportional current I2 ≈ 160 µA/psig.
Calculating √I2 works as follows:
Due to the logarithmic behavior of silicon transistors, base-emitter voltages
Vbe2 = Alog(I1/2) + B, and Vbe3 =Alog(I2) + B, where A and B are constants common to all five transistors in
the LM3046 array. Because addition of
logs is equivalent to multiplication,
(Vbe2 + Vbe3) = (Alog(I1 × I2/2) + 2B).
Series/parallel connection makes (Vbe2+ Vbe3) = (Vbe4 + Vbe5) and, because of
the implicit matching between transistors in a monolithic array, Vbe4 = Vbe5.
Therefore, Vbe4 = Vbe5 = (Alog(I1I2/2)/2 + B). Division of logs is equivalent to inverse exponentiation. Hence,
Vbe5 = log(√ I1× I2/2) + B.
This makes log(I3) = log(√ (I1× I2/2)).
I1/2 = 250 µA, so substitution and exponentiation yields I3 = √(I2 ×250µA).
With the components and circuit
values shown, I3 ≈ 1 µA/knot. With
suitable adjustment of R8, a wide
range of full-scale air speeds can be
calibrated for. If R8 ≈ 10k, for exam
ple, Vout = 10 mV/knot for a 1-V fullscale output at 100 knots. This is just
about right for duty as a primary airspeed indicator in an ultralight aircraft. Of course, suitable adjustment
of R8 can accommodate different
preferences in air-speed measurement units, such as meters per secon
or statute miles per hour.
Supply-voltage regulation for this
circuit isn’t critical and power demand is modest, easily allowing battery operation. The simple power
supply shown will provide more than
100 hours of operation from a 9-V alkaline battery
