# Differences Between Pressure and Gps Altitude

Using GPS to police altitude limits has some potential pitfalls for competitors and organisers. The height recorded by a GPS can be up to 10% higher than the pressure altitude shown on an altimeter. So a GPS may suggest that a pilot has infringed an airspace ceiling when actually he hasn’t.

## Here's the background as to why.

In this discussion I'll ignore instruments that have both a pressure sensor and a GPS receiver. When I say altimeter I mean a simple instrument without a GSP e.g. a Brauniger IQ comp and when a say GPS I mean one with a height output but without a pressure sensor e.g. an MLR.

## I'll start with a few definitions.

Geometric height is the vertical distance between where you are and the sea level datum, as you would measure using a very long tape measure. This is essentially the height data that is output and recorded by a GPS, however the GPS will use the WGS84 ellipsoid as its zero height datum rather than sea level (more on that later).

ICAO define a international standard atmosphere (ISA) with a pressure at sea level of 1013.2mBar and lapse rate (decrease in temperature with increasing altitude) of 6.5degC/1000m. Knowing these two values, the properties of air and the acceleration due to gravity, it is possible to calculate the pressure at any geometric height above sea level. This is shown as the blue line in figure 1.

### Figure 1 ICAO Standard Atmosphere

This standard relationship between pressure and height is used to define pressure altitude. To cope with non-standard pressures the sea level pressure setting in the altimeter can be adjusted so that the altimeter still reads zero at sea level which is equivalent to moving the line in figure 1 up or down to give the correct sea level pressure. However, this only corrects for variations in pressure not temperature so the altimeter still reads a form of pressure altitude, not geometric height.

Geometric height is only used on air maps to define the height of terrain and is not used for any airspace. All airspace is defined in terms of pressure altitude either based on the standard sea level pressure (1013.2mBar) or the actual sea level pressure.

The first difference between pressure altitude and GPS height comes about because the WGS 84 ellipsoid which defines zero GPS height can be up to 100m from the actual sea level, which is used as the reference for pressure altitude. In Europe the WGS84 ellipsoid is around 30m above sea level.

There are further small differences due to errors in each instrument, particularly the GPS for which the altitude measurement is significantly less accurate than the position measurement. GPS height errors will typically be less than 30-50m but can be more especially transiently if signal quality is poor. Altimeter errors will typically be less than 10m but can be up to around 30m and may degrade with age if not recalibrated.

However, the largest differences come about because the change in pressure with geometric height depends upon the air density which in turn depends upon temperature as well as pressure.

If you imagine a 1m cube of still air, it has 3 vertical forces acting on it which must balance (figure 2).

## Figure 2 Forces on a Cube of Air

- A downwards force on the top face equal to the air pressure there (Pt) x the area (1m2) so the force is Pt
- A downwards gravitational force due to the weight of the air in the cube = density x volume (1m3) x g (acceleration due to gravity)
- An upwards force on the bottom face equal to the air pressure there (Pb) x the area (1m2) so the force is Pb

So Pt +(density x g) = Pb

So the change in pressure per meter of geometric height = Pt-Pb = -density x g

What this means is that on a hot day when the air density is lower, the change in pressure (and hence by definition the change in pressure altitude) with increasing geometric height is less than on a "standard" ISA day. The pink line on figure 1 shows the relationship between pressure and geometric height if the air temperature at all altitudes is 25 deg C hotter than the ISA temperature for the same pressure altitude, ie 40deg C at sea level, and around 31deg C at around 5000ft, typical of a fairly hot continental flying day. For this idealised hot atmospheric temperature profile the geometric height (as measured by a GPS) is about 9% higher than the pressure altitude as measured by an altimeter set to the correct sea level pressure.

Figure 3 shows a GPS and altimeter trace from a warm but not excessively hot European day. The pilot has set his altimeter to match GPS altitude at launch. As he climbs above that altitude the GPS progressively reads higher than the altimeter and vice versa as he descends below launch altitude. Figure 4 shows the difference between the two measurements plotted against the GPS height. In addition to the general trend there are other random errors from one or both instruments but these are generally less than 20m.

## Figure 3 Typical GPS & Altimeter Trace

## Figure 4 Differences Between GPS Height and Pressure Altitude

So since a GPS and a pressure altimeter are measuring two fundamentally different quantities, even if they are both 100% accurate they will generally not read the same altitude. The pressure altimeter is measuring pressure and representing that as an altitude based on some essentially arbitrary assumptions about the "standard" atmosphere. Comparing the two is a bit like comparing the straight line distance between two points from a GPS with the trip milometer distance from driving along a winding road between them. Although the two distances are related they will not be the same even if both instruments are 100% accurate, except in the special case of a straight road. Likewise the GPS and pressure altimeter will only read the same altitude if the temperature profile in the atmosphere matches the profile assumed in the standard atmosphere, and the pressure altimeter has been corrected for the actual sea level pressure.

Most electronic varios have temperature compensated pressure sensors but all that does is ensure that the sensor reads the correct pressure as temperature varies. It does not in any way try to compensate for the effect of temperature on the relationship between pressure altitude and geometric height. To do that you'd need to know the complete temperature profile between sea level and your altitude so it is totally impractical.

## The key issues for competition flying are as follows.

- In hot places GPS height can be up to 10% greater than pressure altitude after accounting for variations in sea level pressure so a GPS will tend to show that you’ve busted an altitude ceiling before you actually have. There will be further differences due to errors in each instrument.
- In Europe this will be partly offset by the fact that the WGS84 ellipsoid is around 30m above sea level.
- Setting an altimeter by setting it to the geometric height at launch rather than setting it to zero at sea level (or setting the sea level pressure) can result in an error of up to 10% of the launch height.
- Competition organisers need to understand the differences between pressure altitude and geometric height and must be very clear in briefings about whether any altitude limits that they specify are geometric heights or pressure altitudes and how they will be enforced. There's a bit of a mismatch here as all airspace limits are pressure altitudes but the proposal is to use GPS (Geometric) height data to enforce those limits.
- For instruments with a GPS receiver and pressure sensor, competition organisers must understand which altitude is being recorded by the instrument so that altitude limits can be enforced in a consistent way.