# Gravitational Acceleration and Rising Objects

1. Jan 31, 2012

### Jason0725

So I'm performing an experiment at my university in which we've got to construct a sounding balloon payload to measure the relative changes in gravity for up to 100,000 feet. I'm having a bit of trouble, however, sorting out the math and such.

So the payload is rising, and its position will be tracked by GPS. We've also got a gyroscope, magnetometer, and single-axis accelerometer that we're planning on using to calculate the payload's accelerations.

My dilemma is this: I believe the payload's accelerations would be the "proper acceleration," and the acceleration calculated from the GPS data would be the "coordinate acceleration." So then I could get my change in gravitational acceleration by getting the downward component of my payload's proper acceleration and subtracting the coordinate acceleration from that, right? But the coordinate acceleration would be upward, opposite the gravitational acceleration I'm trying to measure.

2. Feb 1, 2012

### Mentz114

Suppose the accelerometer on the ballon is a spring balance with a lump of lead attached. When it's sitting in the lab the spring balance is measuring the gravitational acceleration.

If the balance is accelerated upwards, the reading on the balance will increase, just as one feels heavier in an elevator accelerating up. So, presumably, if you subtract the GPS acceleration, you'll get the gravitational acceleration.

The problem is that the difference will be very small and probably smaller than your error bars.

3. Feb 1, 2012

### bahamagreen

Just thinking... a rising balloon may only accelerate for a few seconds before attaining a terminal velocity through the air. Then that velocity may change slowly with changes in density. If the measuring package is suspended from the balloon, there may be lateral accelerations to account for because of winds.

I tend to agree that the noise in the data may overcome the measurement.

4. Feb 1, 2012

### D H

Staff Emeritus
I don't think you want to use an acceleration calculated from GPS data. It's going to be noisy.

With a balloon that goes up to 100,000 feet you are only going to get a very localized picture of Earth's gravity field. So use a localized model. You aren't chasing after extreme accuracy with the kinds of equipment you can put on a balloon. This suggests a simple localized and linearized model of gravity: Some acceleration at ground level less a free air correction.

Rather than using canned values, you are trying to back out the ground level acceleration and the free air correction. Some kind of least squares filter would work quite nicely here, either a Kalman filter or a batch least squares. With this, all you need from your GPS is the height above the reference ellipsoid.

I have doubts that a simple one-shot balloon experiment with presumably cheap and lightweight equipment will get you anything beyond this.

Why the magnetometer? That seems out of kilter given that you are only using a single axis accelerometer.