Pressure Sensing 101

05 Oct 2005 Pressure Sensing 101

From: “Richard E. Tasker”
Date: Wed Oct 5, 2005 9:51 pm
Subject: Pressure sensing 101 retasker2000

Caution: Significant technobabble to follow 🙂 ! But you might learn
something…

A quick primer on pressure sensing. First, the basic measurement units
we will use are psi and psia. Psi is a reading relative to some
reference pressure. Psia is a reading relative to an absolute vacuum.
Pressures in the following discussion have been rounded off for clarity
and simplicity (?). Calculate them to the fourteenth decimal place if
you want, but the conclusions will not change.

All readily available pressure sensors ever made measure differential
pressure. Except for some new technologies where the pressure is
indirectly measured by monitoring some sort of parameter that varies
with pressure (heat conductivity, density, electron transport, etc.) it
is impossible to measure pressure without a reference of some sort due
to the physics of the measurement method. Virtually all sensors now
available (for a reasonable cost) use a diaphragm of some sort and a
means of measuring the displacement thereof to measure pressure. This
means that the diaphragm displacement is affected by the difference in
pressure between the two sides – differential pressure.

The common sensors which we consider “non-differential” operate with the
pressure we want to monitor on one side of the diaphragm (pressure port)
and a reference pressure on the other side (reference port). The
reference we use varies depending on what type of sensor it is. There
are three common types.

Absolute, where the reference port is exposed to a vacuum which is
sealed in when the sensor is manufactured.
Sealed gauge, where the reference port is exposed to a sealed cavity
which has some pressure in it – typically standard atmosphere. This is
a “poor man’s” absolute since it is easier to manufacture but works, in
most respects, the same as an absolute sensor.
Gauge, where the reference port is exposed to the atmosphere. In the
case of the sensors we (AST) manufacture, we go to great pains to make
sure that the atmosphere side can easily “breathe”.

A “differential” sensor is precisely nothing more than a gauge sensor
where one can control what pressure the reference port is exposed to.
If we use a differential sensor and leave the reference port open to the
atmosphere it is a gauge sensor.

What happens when we hook these sensors up so we can read out what they
are doing and just leave the reference port open to the atmosphere?

An absolute sensor will measure the absolute pressure that is applied to
the pressure port. At standard atmosphere (sea level) it will indicate
a pressure of 14.7 psia (+/-). If the temperature of the sensor changes
the reading will still indicate 14.7 psia since the trapped vacuum does
not change with temperature.

A sealed gauge sensor will also typically be calibrated to read 14.7 psi
at standard atmosphere (sea level). However, the reading will likely
change somewhat if the temperature of the sensor changes since the gas
or air trapped in the sealed cavity will expand or contract as the
temperature changes. This pressure difference is proportional to the
change in temperature vs the absolute temperature. For example a change
of temperature from 25°C to 0°C will be approximately 25/(273 + 25) or
about 8% of the pressure in the sealed cavity. If this was sealed at
sea level (14.7 psia) then the error caused by this temperature change
is slightly more than 1 psi. – possibly significant or not depending on
what pressure you are measuring.

A gauge sensor will always measure the pressure relative to ambient
atmospheric pressure. So at sea level it will measure 0 psi. Any
temperature changes have no effect since it “breathes” freely with the
ambient atmosphere.

As one goes up in altitude, still leaving the pressure port open, the
absolute and sealed gauge units will read less and less pressure (at
10,000 ft they will read approximately 10 psi). The gauge sensor will
still read 0 psi at 10,000 ft.

So far so good. Now remember that all these sensors will read
“differential pressure” as we apply operating pressures to the sensors.

First let’s look at the oil pressure. The oil pressure is typically
regulated by some sort of valve (typically a small cylinder and spring
combination in a hole that exposes more of a bypass port as the spring
compresses). The valve has a force (on the back side) on it that is
proportional to the spring rate and how much the spring is compressed
plus a force due to atmospheric pressure times the area of the
cylinder. I am not entirely sure what size the cylinder is in the
Subaru, but I would guess that it is significantly less than one inch in
diameter. Let’s assume 0.5″ diameter which means that the area is about
0.2 sq. in. This means that the force on the cylinder due to the
atmosphere is 0.2 x ambient atmospheric pressure, or 2.9 lbs at sea
level and 2 lbs at 10,000 ft. for a difference of 0.9 lbs. The oil pump
will force oil into the oil galleries until the resulting oil pressure
on the cylinder creates a force to just balance this spring plus
atmospheric pressure force. What this means is if the oil pressure is
supposed to be 60 psi, and is (factory) adjusted to or designed to
provide 60 psi at sea level, it will actually be 59.1 psi at 10,000 ft.
– not a big difference. These pressures are the actual internal
pressures the engine will see on the bearings and can also be expressed
as psia (74.7 psia and 74.6 psia).

What happens when we measure this with the typical gauge sensor?

At sea level the sensor will read 60 psi since the sensor reference is
14.7 psia and the actual oil pressure is 74.7 psia (74.7 – 14.7). As
you climb to 10,000 ft. the ambient atmospheric pressure drops to 10
psia so the reference is now 4.7 psi less. The actual engine oil
pressure is now 74.6 psia, but the sensor reference is only 10 psia so
the pressure read on the sensor is 64.6 psi (74.6 – 10).

If the oil pressure control valve was larger (say 1 sq in), the results
would be much different. The actual oil pressure would change directly
proportional to the ambient pressure change (60 psi at sea level and
55.3 psi at 10,000 ft.) – not as good a situation for the engine but
still not a big deal. However the pressure we would read out would not
change with altitude! Doing the same math as above: Oil pressure in
psia at sea level (74.7 psia) and at 10,000 ft. (70 psia). Pressure
reading at sea level (74.7 – 14.7 = 60) and at 10,000 ft (70 – 10 = 60).

So, in answer to your question about the oil pressure, yes, the
indicated pressure does change with altitude, the actual oil pressure
also changes with altitude and what you read is not what you get! On
the other hand, the oil consumption does not vary with the pressure 🙂
and as long as the pressure is some minimum value plus or minus some
relatively generous margin all is well. In other words, don’t worry
about the slightly erroneous oil pressure readings.

The fuel pressure is a different animal because the regulator is
referenced to the manifold pressure, not ambient pressure, while the
fuel pressure sensor we now use is referenced to the ambient pressure.

While I do not know exactly how the fuel regulator responds to the
reference input, I will assume that it responds directly proportional to
it. This would be the desired situation in that it would regulate the
fuel pressure relative to the manifold pressure – providing a constant
fuel pressure across the injector orifices. That is, the fuel injectors
inject the fuel into the manifold at whatever pressure the manifold is
and the fuel flow rate through the injector is proportional to the
difference in pressure across the orifice (fuel pressure minus manifold
pressure – the ol’ differential pressure again).

So… We adjust the fuel regulator at sea level with ambient manifold
pressure (fuel pump on, engine off). Let’s say we adjust it to 30 psi
under these conditions, using the fuel pressure sensor to read out the
30 psi. To keep everything sane in the following discussion, we have to
express all the basic pressures we will use in psia. In this case, the
reference port of the sensor and of the regulator both have 14.7 psia
applied and the pressure port has 44.7 psia applied. So the fuel
pressure sensor will read 30 psi (44.7 psia – 14.7 psia) when the
regulator is adjusted properly and this 30 psi is what the injectors “see”.

When we start the engine, the manifold pressure immediately drops. At
idle, we can assume that the manifold pressure is probably no more than
4.7 psia (approx. 20 inches Hg vacuum in more typical manifold terms).
Using our original assumptions about the regulator function, it will
still be regulating to 30 psi relative to the manifold pressure and
relative to the injectors but this is now 34.7 psia (30 psi + 4.7 psia)
. The pressure sensor will read something else entirely since the
reference to the pressure sensor is still 14.7 psia. The pressure
sensor will now read only 20 psi (34.7 psia – 14.7 psia)!

As we move the throttle towards full, the manifold pressure will
increase until it is essentially atmospheric pressure and the sensor now
reads the same pressure as the regulator is actually providing. Unless,
of course you have a supercharger – in which case the pressure sensor
will read higher than the regulated pressure. At 50 in Hg. the fuel
pressure will be almost 55 psia and the sensor will read almost 10 psi
high (40 psi).

When we start flying and climb the readout changes once again.
Remembering that the regulator is regulating relative to the manifold
pressure, the altitude has no effect on the function – whatever the
manifold pressure is that is what the reference for the regulator is.

Let’s take the same situations we used at sea level but move up to
10,000 ft. At idle, if we assume that the manifold pressure is once
again 5 psia (might be lower since the ambient pressure is lower – or
maybe not) the fuel pressure is still 34.7 psia. But now the reference
port of the sensor is 10 psia so the read out will be 24.7 psi (34.7
psia – 10 psia).

At full throttle, the fuel pressure will now be 40 psia (assuming
essentially ambient atmospheric pressure) and the sensor will read out
30 psi (40 psia – 10 psia), essentially what the fuel pressure really
is. Again, with a supercharger the fuel pressure will be much higher
but the sensor will read out incorrectly. At 50 in Hg the fuel pressure
will still be 55 psia but now the sensor will read out 45 psi (55 psia –
10 psia).

So, with a gauge sensor we have seen pressures from 20 psi to 45 psi for
a fuel pressure that is always 30 psi relative to the manifold
pressure. The pressure switch will respond precisely the same as the
gauge sensor in this example. So if you have it set to switch at 28
psi, it will invariably switch at idle in the above example.

There is really no solution to that problem except to set it low enough
on the ground with the engine off to prevent false trips at idle.

As far as fuel pressure measurement and indication the solution is to
use a differential sensor and connect the reference port to the manifold
where the fuel regulator is connected. That will read out exactly what
the regulator is providing to the injectors.

As far as availability of appropriate sensors (the following is NOT a
sales pitch).

While we do manufacture appropriate sensors (Model 5000) at my company
(www.astsensors.com) and I intend to use one; thanks to all the lawyers
and juries out there, I cannot knowingly sell them for aviation use at
this time. We do intend to get liability insurance for aviation
applications in the future (one of our products will be used on the
Eclipse) and when that happens I will let you know and will provide a
discounted price for anyone that may be interested.

In the mean time, although you will have to pay list price, if you call
one of our sales personnel and ask to purchase a differential sensor for
use on your “RV” to monitor fuel pressure 😉 … Just don’t tell them
you heard about it from me … Unfortunately, I do not know of any
other sources of differential sensors that are suitable for gasoline
exposure that are not prohibitively expensive

One could probably (depending on the specific sensor) modify a gauge
sensor to make it a differential sensor by merely rigging up a way to
connect the manifold pressure source to the reference port. Depending
on the sensor it could be as easy as drilling a hole in the case and
epoxying a tube onto it.

Dick Tasker