Actual Gravity Tests

[sm625]

Using a small steel ball, a relay, a solenoid, a strain gage, a megasampling A/D converter, and a simple microcontroller, it is easily possible to design a simple gravity tester. The relay activates the solenoid, the solenoid releases the ball, the ball drops, it lands onto the strain gage, the A/D converter records the spike from the strain gage, and the microcontroller displays the time difference from when the relay is tripped to the time the A/D converter records the hit. A ball dropped from 3 feet will yield a time of roughly 438.521mS. If you take this device to the top of a 500ft building and run the same test, the new result should read 438.532mS. But has anyone actually tested this? I dont mean with satellites or fancy gizmos, just measuring the actual freefall times in this way? I know geology affects the reading, as does latitude, but I'm only interested in the height component's effect on gravity.

 

[William Gaatjes]

That should be possible. With an accurate time base (calibrated crystal frequency and in a temperature controlled box) and exactly the same heights used, you could notice the difference in gravity at different spots of the earth.
The only difficult part is that there must be absolutely no wind. Since then when there is wind, the path of the steel ball travels will deviate from a straight line. That means longer travel time because of the angle and Pythagoras. You would need a sensor that could determine the position of the ball when landing for correction calculations.

 

[sm625]

Yeah it would have to be enclosed in a 1'x1'x3' plexiglass box, with maybe a little door on the bottom to retreive the ball, and a hole on the top to reset it. It could even be vaccum sealed with a pinball type action to shoot the ball back up to the solenoid. But that is far beyond the accuracies that I'm looking at.

Another thing I'm looking for is any scientific papers pertaining to gravity measurements at the same location but at different heights. For example, someone measures gravity at the lobby of the Sears/Willis tower and then travels to the top and does the same measurement. I cant find any sort of papers and that is surprising to me. Surely somebody must have done this using a traceable instrument and documented it?

 

[DrPizza]

That should be possible. With an accurate time base (calibrated crystal frequency and in a temperature controlled box) and exactly the same heights used, you could notice the difference in gravity at different spots of the earth.
The only difficult part is that there must be absolutely no wind. Since then when there is wind, the path of the steel ball travels will deviate from a straight line. That means longer travel time because of the angle and Pythagoras. You would need a sensor that could determine the position of the ball when landing for correction calculations.

If the wind was horizontal, it wouldn't affect the time of the fall. The vertical component of acceleration is the same.

I'm kicking myself for not reading the OP closely enough - I didn't see that he had done the calculation on what the time should be at 500 feet. I assumed 1.000000 meters and his local value of g to be 9.810000 at ground level. I too got a difference of 1.1E-05 seconds. I did not take into account any centrifugal effects of the higher elevation.

But, I have to ask, how repeatable is the experiment? If you were to pick up the equipment, carry it, and put it back in place, is the time going to be the same, +/- one digit in the last unit place recorded? I.e, your equipment is rigid enough and doesn't flex? Just a quick back of the napkin calculation, a difference of couple hundredths of a millimeter in distance will have the same effect on time. Coincidentally, this number was nearly the same as the thermal coefficient of expansion of aluminum - thus, a difference in temperature of 1 degree C would result in that difference in distance, assuming a device made of aluminum 1 meter in length. (Rough calculations.) But, it implies that your experiment would be very sensitive to temperature changes.

 

[MrTeal]

Yeah it would have to be enclosed in a 1'x1'x3' plexiglass box, with maybe a little door on the bottom to retreive the ball, and a hole on the top to reset it. It could even be vaccum sealed with a pinball type action to shoot the ball back up to the solenoid. But that is far beyond the accuracies that I'm looking at.

Another thing I'm looking for is any scientific papers pertaining to gravity measurements at the same location but at different heights. For example, someone measures gravity at the lobby of the Sears/Willis tower and then travels to the top and does the same measurement. I cant find any sort of papers and that is surprising to me. Surely somebody must have done this using a traceable instrument and documented it?

At the very top of the Sears tower you'd expect the acceleration due to gravity to by 0.99986 of that at ground level, so as you said the time difference will easily be measurable. Your big challenge will be designing an experiment that can get the required level of accuracy.

Ideally you'd have a system that keeps the ball perfectly stationary prior to the input signal, and then exerts no force on the ball the instant that the signal arrives. If that isn't possible, having something that has a precise, fixed delay would be acceptable as well. Implementing that in a real system would be easier said than done though, especially in a way that doesn't impart any downward velocity to the ball. Similarly, you'd want a measurement system at the bottom that trips the uC at the instant the ball first touches, or at least with a predictable delay after the ball hits. A strain gauge might not be the best way of measuring that, though you'll definitely get a signal. You might have a non-linearily in your strain gauge response time as well, since the velocity and energy of the ball at the bottom will be different at different elevations.

Also, as MrPizza said, you'd have to be careful to keep the path the same for different elevations and temperatures. Building the box out of glass (quartz better, Zerodur/Sitall probably the best) would help, as would using a vacuum pump to evacuate it and remove the air density variations with altitude.

tl;dr, should be possible, difficult to implement successfully.

 

[Squeetard]

People have been using gravity meters for geology, archeology, oil and mineral searches for 30 years or more.

 

[IronWing]

Back in geophysics class, we had to calculate the effects of differences in gravity among different Olympic venues on distances achieved by ski jumpers. The effects of gravitational variation were of the same order of magnitude as the range of distances among the the medalists over the different locales.

 

[BarkingGhostar]

Could I just accept the work of prior folks?

 

[sm625]

Could I just accept the work of prior folks?

As I said in post #3 I would like to read any published and peer reviewed papers pertaining to gravity measurements at the same location but at different heights. For example, someone measures gravity at the lobby of the Sears tower and then travels to the top and does the same measurement. I cant find any sort of papers.

 

[DrPizza]

Back in geophysics class, we had to calculate the effects of differences in gravity among different Olympic venues on distances achieved by ski jumpers. The effects of gravitational variation were of the same order of magnitude as the range of distances among the the medalists over the different locales.

Intuitively, I would have said there would be a difference. However, a year ago a bunch of us physics teachers were experimenting with a contest - fine tuning it so we could run it with students. In essence, a steel ball was going to swing down, attached to a thread - like a pendulum. Right at the bottom point, there was a razor that cut the string, turning the ball into a projectile following a parabolic trajectory, starting at a certain height above the floor. Students had to place a target on the floor where the ball would hit. What, at first, was non-intuitive to me, was that if you solved all the equations for the range, prior to plugging in any numbers, gravity dropped out of the calculation completely. Now, my first instinct in the case of a ski jump is that the local value of gravity shouldn't matter. Of course, with a smaller value of g, the launch velocity will be lower. But then, the jumper will have more "hang time" because the launch velocity will be lower.

So, I'm curious - was your analysis based on an assumption of equal velocities at the base of the jump? Or did you account for the gravity in all aspects of the jump, and my intuition is wrong? And, if your analysis was that rigorous, did you account for less drag force in the lower gravity environment due to a lower (presumably) air pressure, and because the drag would be proportional (in many models) to the square of the velocity?
Parent-teacher conference day here - yes, I'm that bored that I'm working these things out. I think I've seen 2 parents in the school - with grades being online, and quicker communication via email throughout the year, that's to be expected.

 

[sm625]

Right at the bottom point, there was a razor that cut the string, turning the ball into a projectile following a parabolic trajectory, starting at a certain height above the floor. Students had to place a target on the floor where the ball would hit. What, at first, was non-intuitive to me, was that if you solved all the equations for the range, prior to plugging in any numbers, gravity dropped out of the calculation completely.

I dont see how gravity drops from the calculations. Gravity is responsible for the horizontal component of the velocity at the moment the string is cut, and thus it is required in order to calculate the distance traveled.

 

[serpretetsky]

I dont see how gravity drops from the calculations. Gravity is responsible for the horizontal component of the velocity at the moment the string is cut, and thus it is required in order to calculate the distance traveled.

I didn't do the calculations, but it doesn't seem far fetched:

Increase gravity -> faster horizontal trajectory, but also faster falling speed once string cut
decrease gravity -> slower horizontal trajectory, but slower falling speed once string cut

I think if I tried to build my own gravity measuring device I would try to make it static to avoid having to deal with wind and precising timing. Something like trying to measure the force a 1kg ball exerts at sea level and then the same ball at 500meters high. Would still have to compensate for air buyouncy at different heights though.

 

[Biftheunderstudy]

I don't think measuring the freefall time is the best way to measure local gravity. Mostly due to DrPizza's objections, but this was figured out centuries ago.

A much more precise and repeatable way of measuring gravity is to use a pendulum, again figured out centuries ago. Incidentally, since a lot of this stuff was done a long time ago, it'll be hard to find any papers where people actually bring an apparatus and move it around to measure gravity. -- I'm sure there are people who have done it, but I doubt it is publishable at this point.

You may have some success by looking for things like gravity probe and the like. We routinely make maps of the Earth's gravity using satellites.

EDIT:
I should point out that this is not how we measure gravity now. For that I suggest reading this: https://en.wikipedia.org/wiki/Gravimeter

 

[Carson Dyle]

I just saw this thread. When I lived in Boulder, Colorado I had a roommate whose job was to measure gravity. He was part of a small crew of three or four guys who traveled all over the world. And I mean _all_ over. Every continent, remote desert locations, the sides of mountains, above the Arctic circle, Nepal, Brazil, Australia, Norway ... everywhere. He told me that they had permanent survey markers in hundreds of different places around the globe and every few years they'd return to a marker, set up, and take measurements for a day or two.

They used a gravimeter as described above. Basically a vacuum cylinder in which a mirrored weight is dropped. The vacuum part is critical, as variations in atmospheric conditions would render the test results useless.

I believe that the government agency he worked for in Boulder was NIST (National Institute of Standards and Technology). From what he told me, NIST made the data that they gathered available to anyone. Commercially, it was typically used for things like oil, gas and mineral exploration. Non-commercially, I believe it was used to study things like plate movement through the variations in gravity seen over time.