John Hansman and Oliver Smoot on Measurement at MIT - 1995

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HANSMAN: The invention of the metric system in 1790 improved matters somewhat by basing units of measure on more widely agreed upon standards, like the circumference of the Earth. Back at the turn of this century, Lord Kelvin, namesake of the international temperature standard, said it best. One has but a poor understanding of that which one cannot measure.

Today we try to have rational, simple, and consistent measurement systems based on sound scientific principles. The goal of this video series is to introduce you to the principles of measurement. But we'll also show you some of the standard techniques and equipment.

The series is designed as a basic introduction to measurement. It should help you whether you are attempting to learn about measurement as training for new job, or you are trying to solve a particular measurement problem. The series may not give you all the answers. But after watching, I hope that you will at least be able to ask the right questions.


I'm sitting up in the summit of Mount Washington. And the actual summit is located underneath this reference data marker placed here by the US Geological Survey. We're going to talk about techniques to measure distance, velocity, and acceleration using techniques as simple as something like this ruler, and as sophisticated as this global positioning system unit.

The fundamental standards for the measurement of distance, velocity, and acceleration are length and time. I've come here to the museum at the National Institute of Standards and Technology to show you a few examples of current and historical standards of length and time. The museum has a mission to preserve the historic evolution of physical measurement.

Now, the current standard of time is the second. And it's defined in terms of the atomic transitions of caesium atoms. Caesium atoms are part of an atomic clock. And this is one of the original cesium ovens. Cesium was heated, and a cesium beam would be emitted from the front of this oven into the atomic clock.

Now, it's not practical to have atomic clocks for day to day time measurement. And today we have very good working standards in terms of quartz crystal oscillators, which are seen in things as common as my wristwatch. Now, the international standard for length measurement is the meter. And the meter was established as an international standard at the International Conference of Weights and Measures in 1889.

Because the US was a member of that conference, it received one of the prototype meters, which I have here. This prototype was one of 31 that was built at that time. And the one that was closest to the existing meter was preserved in Paris as the international standard. And each of the countries that participated received at least one of these meter bars.

The US received number 27. This meter bar is built out of platinum and iridium and is accurate to within 1.6 microns at zero degrees centigrade. It's 1.6 microns short of a true meter. Now, this was the US standard from 1893 to 1960. And the current standard for the measurement of length, or definition of a meter is defined in terms of the speed of light.

Some historical length standards are based on people. For example, this is a replica of an Egyptian royal qubit, which was used about 1500 B.C. And it was based on the length of the forearm of the pharaoh Amenhotep. At MIT we also have a unit of length, which was based on a person. And we've arranged to talk to Oliver Smoot about how this happened.

I had the privilege to meet with Oliver Smoot, who is a living length standard. And Ollie, this honor is normally reserved for kings and pharaohs. How did it happen to you?

SMOOT: Well I don't know about them. But I got it because I'm short.

HANSMAN: You're short.

SMOOT: Well, I don't know. 5'7" I guess is below average these days.

HANSMAN: How did that get you to become a length standard?

SMOOT: When I was a freshman at MIT we lived in a fraternity house on the Boston side, Lambda Chi Alpha. And to get to class you had to go across the Mass Avenue Bridge, which is a long bridge. You know exactly, I'm sure. And our pledge master said, he was late too often. So he wanted us within a week to measure the bridge. And he made all 14 of the freshmen stand up, and looked at us, and said, Smoot, you're the shortest. So we'll do it in Smoots.

HANSMAN: Okay, and how many Smoots was it across the bridge?

SMOOT: 364.4 and an ear.

HANSMAN: How did you get the 0.4 and an ear?

SMOOT: Well, actually there-- when we got to the last expansion joint, there's an actual end to the bridge there. It came up to about my knees. So we did 0.4. And decided that since we knew there were errors in the measure, that we'd be honest engineers and put a Greek E, which means error measurement. And then we decided that most people wouldn't know what that meant. So we wrote an ear. Because maybe that's about the right amount of error.

HANSMAN: There's a little bridge here at the plaza at NIST. I wonder if I could talk you into making a little measurement of this bridge in Smoots.

SMOOT: Well, if it weren't for MIT being involved in this, I don't think so. But sure.

HANSMAN: All right. This will be a credible measurement. Now, let's start at the edge of the water, over here.

SMOOT: Okay.

HANSMAN: Okay. Okay, Ollie. I'm going to put a reference mark here at the start of the bridge over the water. So.

SMOOT: All right. Let's see what we get.

HANSMAN: Okay, yeah. Let's see what you did. All right?

Okay. Now.

SMOOT: Aim for the top.

HANSMAN: All right. Your head's the top.

SMOOT: Okay.



Okay, Ollie. We've now officially measured the bridge here at the National Institute of Standards and Technology. And it looks like you're about 1/10 of a Smoot short of 4.

SMOOT: Yeah.

HANSMAN: So we're 3.9 Smoots.

SMOOT: Plus or minus an ear.

HANSMAN: All right. Plus or minus an ear. All right. Now, you said you're about 5' 7". And so one Smoot is about 5 feet 7 inches. You think you're still 5' 7"? Is the Smoot a stable reference standard?

SMOOT: Maybe, because my hair is thinner. I don't know. Sometime, I guess I'll get shorter. But so far, it seems to be about the same.

HANSMAN: I've come to one of the experimental research facilities here at MIT's Lincoln Laboratory to talk about distance, velocity, and acceleration measurement. The antenna you see above me is an air traffic control radar, which is used to measure the position and velocity of aircraft. This is the radar controller station at the Lincoln Laboratory experimental radar facility.

Perhaps the simplest method for measuring distance is by the use of calibrated length scales, such as this tape measure or this ruler here. Now, the maximum resolution you can get with a calibrated scale, such as this ruler, depends on the minimum graduation of the scale. You can see this ruler is calibrated both in centimeters and in inches. And the finest graduation of the centimeter scale is 1 millimeter. So this system is really only usable for accuracies down to, say, a fraction of a millimeter.

Now, rulers and tape measures are good for measuring linear distances where you can actually put the edge you want to measure right up against the scale. So you can get a fairly accurate measurement of the dimensions. Now, you get into trouble if you try to measure something like the diameter of this pipe with a ruler.

The problem is that, because you can't put the edge of the pipe right up against the ruler, you run into what we call parallax error. If you move your head, what happens is that the apparent edge of the pipe will move around. So you can't get a very accurate measurement.

Now, we can actually use something like this caliper, here, to measure the dimension of the pipe. What I can do-- let me just do it from the top, here-- is squeeze down on the pipe with this caliper. And you can see this is an electronic caliper, which measures the diameter at about 15.98 millimeters. I can also flip the calipers over and use these feelers to measure the inside diameter of the pipe. And the caliper also has a probe here that can be used for measuring down inside the pipe, the depth of the pipe.

Now, I could also use something that we call a micrometer. This is very commonly used in mechanical measurements, machining, things like that. And essentially, what it is, is a calibrated screw. What I do is I twist the screw down until it squeezes on the pipe. And when the screw hits the pipe, it stops rotating.

Now, because I have a fair amount of mechanical advantage twisting the screw, I need to be careful that I actually don't deform the pipe-- squeeze it so much that I deform it. And the way I do that is by using this little knob here, which is a spring-loaded knob. And essentially, what I do is I rotate the screw using the spring-loaded knob. And it always applies the same amount of torque. So I essentially get the same tension on the screw every time. And it makes the measurement repeatable.

Now, it's common for machinists to use something called a dial gauge here. And essentially, what the dial gauge does is I have this plunger that pushes up against the object. And it will rotate the dial. So there's a very fine mechanism inside the gauge that will make a measurement of the position and show it on this needle, here. And you can see that just my jiggling around here as I talk is causing the system to jump.

Now, because the mechanism is very fine, what happens is that sometimes the needle zero position will shift. And you can see that I can just rotate the dial, here, to re-zero the instrument.

Now, for some applications, you want an electrical output rather than a mechanical output of position. And there are different ways you can do this. One common technique is by using a potentiometer. And they're are, in fact, many potentiometers in this oscilloscope.

All the knobs, here, are connected to potentiometers, which are essentially just resistors. And as I rotate the position of the knob, what I'm doing is changing the value of the resistance. So you can see, as I change the position of the knob here, what I'm doing is changing the resistance, which then shows up as a change in voltage on the face of the oscilloscope, here. So if I change it a lot, you ought to be able to see that show up on the scope.

Now, this is a measurement of rotary position. But I also am interested, sometimes, in linear position. I can also use a potentiometer there. But we can use a technique called a Linear Variable Displacement Transducer, or LVDT.

Now, what an LVDT is, is essentially an inductor, which is in this metal core, here. And inside the inductor is a magnetic material-- I think, this case, it's nickel-- which goes down inside the inductor. When it does, it changes the inductance, which is measured by a circuit. The circuit is powered by the small power supply here and is actually inside the metal tube.

The output of the circuit is a voltage, which I'm now showing on the oscilloscope. And you can see that if I change the position of the plunger, I get an electrical output of voltage. Okay. If I pull the core too far out, you can see that the instrument saturates. Okay. So its usable range is just a few inches, here, in the middle of the motion.

So far, the smallest distances we've talked about measuring are a thousandth of an inch or a fraction of a millimeter. Sometimes, you need to make measurements more accurately. And to do this, you can't really use mechanical techniques. However, you can use optical techniques.

For example, this laser here has a-- you can see the red dot on my hand-- has a wavelength of 633 nanometers, which is about 0.6 millionths of a meter. And by using interference techniques, we can make measurements on that level of accuracy. Now, there are many different types of interferometers. And what I want to do is talk to you about a simple one, just to give you a feel for the concept.

This is an example of a Michelson interferometer, which can accurately measure the difference between two paths. Light comes from the laser and is split at a beam splitter into a measurement path and a reference path. The light goes out and is reflected off of a mirror and sent back to the beam splitter along both paths. The light is then recombined and picked up in a detector, which measures intensity of the combined light.

Now, if the paths are identical, the waves from the reference path and the measurement path will be in phase and will add together. However, if the paths are different by a quarter of a wavelength, what will happen is the waves will actually cancel-- will come back 180 degrees out of phase and cancel-- so there'll be no intensity at the detector.

So as the measurement path increases in length, what will happen is the intensity measured at the detector will go through minimums and maximums. We call these fringes. And by counting the number of fringes, you can actually measure the change in length along the measurement path. And again, as you can see, this can be accurate to a fraction of a wavelength, which is very small distance.

Many techniques for measuring distance use the principle of time of flight of some wave to make the distance measurement. For example, this ultrasonic distance measuring unit, here, is used for measuring the dimensions of rooms.

So when I push this button, what happens is an ultrasonic wave is emitted from this transducer, is sent out, and bounced off the wall. The reflected wave is picked up by this second transducer, over here. If I measure the round trip time, I can figure out the distance to the wall.

The distance is essentially the round trip time, times the speed of sound, divided by 2 because it was the out and return time. Now, that measurement will be fairly accurate if you know the speed of sound in air. Now, the speed of sound is about 300 meters per second. However, it depends on the temperature. So this measurement will only be accurate if you are at the temperature that the unit is calibrated for or if you correct for changes in the speed of sound.

Now, we actually looked at another ultrasonic measuring unit when we were down at the Omega Engineering labs. And let's go look at that now. This is an ultrasonic distance and level measurement system. And what happens here is that there is an ultrasonic transducer in the top of the unit, which transmits an acoustic wave, which reflects off of the object we're trying to measure and comes back down into the unit.

The transducer actually looks something like this. As I move the plexiglass plate, here, you can see that the distance is shorter. So it takes less time for the wave to go up to the plexiglass and back. Now, the beauty of this method is that you don't need direct contact between the sensor and the object you're trying to measure.

Acoustic time-of-flight techniques can also be used for making distance measurements in fluids, such as water. Now, the speed of sound in seawater, for example, is much faster than air. It's about 1,500 meters per second. And these techniques are commonly used in sonars and depth finders on ships and submarines.

One of the important distance measurements they make on this vessel is the amount of water under the keel. Now, they actually have several sensors on board the vessel that use sonars or depth finders to figure out the distance. They all work on basically the same principle.

Over here, there's a depth finder that says 22 feet. Now, the way they work is an acoustic wave is sent from the bottom of the ship down through the water. It bounces off of the bottom of the harbor and is received by a transducer in the bottom of the ship. By knowing the speed of sound in the water and the round trip time, we can figure out the depth under the keel.

This radar unit uses time-of-flight techniques with radio waves. This unit has about a 10-centimeter wavelength. And for wavelengths between 1 and 30 centimeters, we normally call these microwaves.

Now, basically, the way this works is there's an antenna up in a tower above this building, which transmits radio waves out. And the radio waves are reflected by airplanes flying around the Boston area. Because the radio waves aren't attenuated in air as strongly as acoustic waves, this technique is good for much larger distances. Also the radio waves travel much faster.

So the radar, here, is currently set for range of about 60 nautical miles. And it's common to use radars at even longer distances. In fact, we measure the distance between the Earth and planets using radar techniques.

Now, so far, we've only been talking about measuring distance. But you can see in the radar plot that the radar also measures the direction to the target. We do this by rotating the radar antenna. And let's go up to the tower and take a look at the antenna.

I'm up here on the antenna platform of this airport surveillance radar. And the antenna above me is spinning at 4.8 seconds per revolution. Now, if I shut off the antenna, it'll stop. We can take a look at how the antenna actually works.

Now, if you look closely, you can see that there are two transmitting and receive horns at the focus of the parabolic antenna. Microwaves are emitted from the transmitting horn. They go out and are reflected off the parabola and focused into a relatively narrow beam, at a beam width of about 1.4 degrees. Now, the antenna also works the other way, too. So microwaves reflected off of targets will come back and be focused into the receive horn.

Now, you'll notice that the antenna is wider horizontally than it is vertically. That's because, for this type of radar, we actually want a narrow beam horizontally. But we actually want a defocused or broad beam vertically, so that we get what we call a fan beam. And that allows us to scan all altitudes at one rotation. Some types of radars or some satellite receivers actually have a circular parabolic antenna. And that gives a very tight beam in both horizontally and vertically-- what we call a pencil beam.

Let's now take a look at a very basic radar display. What I have here is what we call Plan Position Indication display, or PPI. In the PPI, the antenna location is at the center of the display. And you can see the rotation of the antenna as it rotates in what we call the azimuthal direction.

Each of the aircraft targets that the radar sees shows up as a what we call blip. And if you look carefully at the blip, you can see some features that indicate the uncertainties in the measurement. If you'll notice, the targets show up wide in the azimuthal direction but very narrow in the range direction. And what that tells you is that the range measurement of the radar is much more precise than the angle measurement or azimuthal measurement. So the targets show up as these sort of spread out targets in the azimuthal direction.

Now, this simple radar screen just shows the primary returns from the targets. And if we look over here, there's a more modern-- in fact, this is a research display-- showing some of the other information the air traffic controllers get. Now, let me orient you to the display, here.

Again, the radar location, here, is at the center of the display. And you can see range rings. Here's one 10 nautical miles out from the radar. Hanscom Airport is located here, right next to the radar. And you can see the runways at Hanscom. If you look down to the right, you can see Boston Logan Airport, again, the runways showing as white lines. And there are some light gray lines, which show you the coast and some of the main roads around Boston.

Now, if we look at one of the aircraft targets, you can see that there's much more information here than just the blip we saw on the other radar. First off, the best estimate of the location of the target is shown. And there's some secondary information you can see, over here.

Now, most of the aircraft flying around Boston actually have equipment on board to enhance their radar returns. And this equipment's called a transponder. And what it does is, when it receives the radar pulse on board the aircraft, there is a second transmitter on the aircraft that sends a return pulse, which is much stronger than the basic reflection that you would have from what we call a primary target.

Now, along with that pulse, the aircraft sends down some information. You can see this target here. The top line is the identification number of the target. So it's sending down a code of 5153. And below that identification number are three digits, which indicate the altitude of the target. So this aircraft is at 2,000 feet above sea level.

This radar also infers the velocity of the aircraft from radar returns. So this little trail, here, is essentially the last 10 hits that the radar has had on the target. So again, that's the last 48 seconds of data from the target. And by the way, I should have mentioned, I've frozen the display here so we could look at it.

So based on those last 10 hits, the radar has calculated that the target is moving at about 110 knots of ground speed. And it's moving to the west. So the air traffic controller can figure out not only the location of the targets, but where they're moving and if there's any problems with collisions.

Now, radars are used for other applications. For example, we can use radars to reflect off of rain and precipitation. And if you look over here, you can see that I have a computer output of a radar down in Florida, which happens, this morning, to be looking at a hurricane which is just hitting the panhandle of Florida.

We can also use radars on other vehicles, such as ships. And let's now go down to the NOAA research vessel, Albatross, to look at the radars on board that vessel. This is the radar display on the bridge of the NOAA research vessel, Albatross IV. This is a display of a primary radar, with the antennas mounted on top of the bridge, here. As the radar rotates, it sends out signals, which are bounced off of either ship targets or land targets. And it can give us a picture.

Now, the radar is actually used for two purposes on the ship. One is to navigate, and the other is to avoid colliding with other ships or boats. We're now moored in Woods Hole, Massachusetts, heading south. And I've set the display up here at about a six nautical mile range. And you can see the coast of Martha's Vineyard across Vineyard Sound, here. You can also see, if you look closely-- in fact, let me increase the range, adjust the display a little bit-- you can see the black area is the channel through Woods Hole.

Now, as I said before, we also use the radar to avoid targets. And the dots that you see in the black are actually individual ships or boats. If I increase the range a little bit more, you can see a couple things in the display. First, these straight lines in front of us are actually the jetties out in front of the ship.

And you can see a few targets. I have one on the right, here. Let me mark it. There's a little cursor. And if I mark this target, you can see that there's a boat 0.17 nautical miles to my right. It's on the 078 degree bearing. If we look out there, we can see that the boat that I marked was actually the 12-meter yacht, Shamrock, which is moored in the harbor next to us, here, at the dock.

We've talked about techniques for measuring distance using acoustic waves and radio waves. But you can also use time-of-flight techniques with light or infrared radiation. And in fact, much of the equipment that's used for land surveying uses time-of-flight techniques of infrared radiation. Now, I made arrangements with one of the surveyors who works with MIT to show you this equipment by measuring one of the buildings at MIT.

Distance measurement is an important part of surveying. And Ken Strom, who's a professional land surveyor for Cullen Engineering, has agreed to help us do a survey problem here at MIT. What I'd like to do-- what I thought would be fun-- is to try to measure the exact height of the Great Dome, here, behind me. So, Ken, how do we have to-- what do we have to do, to do this?

STROM: Well, what we did was we established a point over here, which has a known position. And we also established an elevation on that point by turning on it, using differential leveling techniques from a deep benchmark, which was established in 1927, located near the corner of this building right behind us, here.

HANSMAN: Okay. So we know the height of this point. And we can then measure the difference between this point and the top of the Dome.

STROM: Yes. Utilizing our total station instrument, we can establish a difference in elevation between the sidewalk, here, and the top of the dome.

HANSMAN: Surveying requires a measurement of both the distance and direction from the known point, or reference mark, to the point you're trying to measure. Traditionally, we would use something like this steel tape to measure the distance and an instrument called a theodolite to measure the direction of the distance. Nowadays, it's very common to use something called a total station instrument, which combines an electronic measurement of the distance with an electronic measurement of the angles.

Now, the way this particular unit works is it has an infrared signal, which is emitted from these optics. The wavelength of the infrared signal is about 0.9 microns. And that wavelength is chosen for eye safety reasons.

What happens is the infrared signal comes out from the unit and is reflected back by a reflector that we set at the measurement point. This particular reflector, here, is a prism. And so we measure the distance from the instrument to the reflector by measuring the time it takes the infrared signal to go out to the reflector and go back.

And that round trip time is, essentially, the distance divided by the speed of light. Now, the speed of light in air is the speed of light in vacuum, about 3 times 10 to the eighth meters per second, divided by the index of refraction of in the air. And so we have to correct for both the temperature and pressure, which influence the index of refraction.

Now, the reason why we use a prism is that we want to make sure that we have a good signal going back to the instrument. If I use something just like a mirror, if it was misaligned, I might run into a problem. So this prism is what we call a corner cube. If we send the light into the corner, no matter which direction it comes from, it'll go straight back out at the instrument. It's a very common technique. In fact, there are some corner cubes set up on the moon that we use to measure the distance between the Earth and the moon.

So, Ken, what we need to do here is find the height of the instrument before I go up in the Dome to set up the prism.

STROM: Yes. As we mentioned earlier, we established an elevation of our reference mark with relation to mean sea level datum. And that was done via differential leveling techniques. And we've established an elevation of 10.02 feet on the reference mark.

And what we will do is measure up with a ruler to an index mark on the instrument. And that will-- we're measuring 5.36 feet above the reference mark, which establishes an elevation of the instrument of 15.38 feet above mean sea level.

HANSMAN: Okay. I've got the prism up here. I actually had to pull it up on a line. And I set it up on this tripod, which is right over the middle of the Dome. And what I'll do is I'll try and align it to Ken. And, Ken, do you have a good line of sight to the prism? Ken, do you have a good line of sight to the prism?

STROM: John, I can see you through my crosshairs. Over.

HANSMAN: All right. Good. All right. I'll just secure it here. And I'll be down in a minute to make the measurement.

STROM: Okay.

HANSMAN: Okay. I think we're stable. It's pretty windy up here, so we've tied down the prism. And I'll head down now. And we'll see what the height of this place is. Okay. Ken, now that I have the prism set up on top of the Dome, we need to line up the instrument on the prism?

STROM: Yes. Yes. The prism, now, is in the crosshairs.

HANSMAN: Okay. And if we press this angle button, what we see is that the angle of the line of sight from the vertical, which we call the zenith angle, is what?

STROM: 77 degrees, 44 minutes, and 5 seconds.

HANSMAN: Okay. And if we make the range measurement.

STROM: Yes. The slope measurement is 693.215 feet.

HANSMAN: So that's the distance between the instrument and the prism.


HANSMAN: And the actual height is that distance times the cosine of the zenith angle--

STROM: Correct.

HANSMAN: --which now is 147.275 feet.

Before I take down the prism, I figured we might as well take a look around while we're up here, on top of the Great Dome. You can see the Green Building at MIT. And across the Charles River, you can see the skyline of Boston. There's the Hancock Tower and the Prudential Tower. And down there, you can actually see the Mass Ave Bridge, or the Harvard Bridge.

Well, when we had Ken here, I couldn't resist asking him to come out to the Harvard Bridge to see if we could see how long the bridge is in feet, to compare that with Smoots. Because the bridge is curved, we actually had to set up the station in the middle of the bridge. And we put prisms on both ends. So, Ken, why don't you go ahead and see if you can measure the first prism.

STROM: 1,014.53 feet.

HANSMAN: Okay. So that's the distance from about the middle of the bridge to the other-- to the north end. And what we'll do is we'll switch it. And we'll shoot the other side. Okay. Then we'll go ahead and make the measurement here. Okay. I got it lined up. Let me measure. Okay, Ken, it's 1,008.27 feet.

STROM: 1,008.27.

HANSMAN: Okay. So the total length of the bridge is--

STROM: We had 1,014.53 heading towards Cambridge. So the total would be 2,022.8 feet.

HANSMAN: Okay. So and that's equal to 3--

STROM: 364.4 Smoots.

HANSMAN: And an ear.

STROM: Yes. One ear.

HANSMAN: One very important type of distance measurement is navigation or locating your position in space. Now, in order to do this, you need some sort of coordinate system. On the surface of the Earth, we use, essentially, a spherical coordinate system because the earth is approximately a sphere.

Now the system we use is the latitude-longitude system. 0 degrees latitude is, essentially, the equator. And it rotates in angular measurement, from the center of the Earth up to 90 degrees at the North Pole, and 90 degrees south at the South Pole.

Now, longitude is defined in terms of east-west position. And 0 degrees longitude is in Greenwich, England, very close to London. And again, longitude goes east and west, from that 0 position to 180 degrees at the International Date Line in the middle of the Pacific.

Now, our location, here in Boston, is-- let's find Greenwich again-- is about 70 degrees west of Greenwich, England, and again, about 45 degrees north from the equator. So our latitude is 45 degrees north, and our longitude is about 70 degrees west.

Now, there are many different ways we can measure position, ranging from celestial navigation techniques, where we locate our position on the Earth with regard to stars, such as the North Star or other stars in the sky at night. We can also use radio navigation techniques, where we measure our position with regard to radio beacons on the Earth.

But perhaps the most important new technique is something that's called a global positioning system. This is a small Global Positioning System, or GPS, receiver. Basically, GPS is another time-of-flight technique using radio waves. But the transmitters are mounted on a constellation of satellites, which orbits the Earth.

Right now, there are about 24 satellites in the constellation. And they're designed such that, at any one time, you should be able to see somewhere between four and eight satellites. A computer in the receiver knows where all the satellites should be at any one time. So by measuring the distance to several satellites, you can figure out your location.

Now, you actually need to measure the distance to at least four satellites. And that's because the clock in the receiver is not as accurate as the clocks on satellites. So by making four measurements, we can resolve the three components of position-- say, north, east, and down-- and also correct any uncertainty in the receiver clock.

Now, the accuracy of the GPS depends on the geometry of the satellites. In order to get a good measurement, you'd really like the satellites to be spread out. If all the satellites were in the same position, you'd essentially just be making the same measurement four times.

So you can see in this figure here, if we just look at two satellites, if I'm a certain range from satellite A, I could be anywhere on this line with some uncertainty. Now, if I measure from satellite B, I could be on this line. And my position would be in the region covered by the intersection of the two lines. But I could be anywhere within the intersection of the two uncertainty bands.

Now, if the satellites were close together, you can see the region of uncertainty becomes much larger. And this effect is called the Geometric Dilution of Precision, or GDOP. And it's normally monitored by the receiver.

Now, if the GDOP is too large, or if you can't see enough satellites, then your receiver should warn you that your measurement of position is unreliable. Now, there are other factors which can influence the precision of a GPS measurement. And one of those is the accuracy of the receiver.

Now, this receiver uses what's called a civil, or C/A, code. And most civil receivers use that code. The military uses another code, called the P code. And the civil C/A code is intentionally degraded by the military for political reasons. So that measurement will only be accurate to within a few hundred feet.

And we actually checked this by taking this receiver up on top of the Great Dome to measure the GPS position and compare it with Ken's surveyed position. This is a civil GPS unit, so it only uses the C/A code. You can see, here-- here's the antenna. Here's the unit-- right now there are six satellites available to us and potentially in view. And the GPS is locked up on all six satellites.

Okay. So what we'll do is we'll now press the navigation page. And we can see that the GPS only thinks we're 37 feet above sea level. You'll see that drift around a little bit as the satellites move. However, the latitude and longitude are also displayed. We're 42 degrees, 21 minutes, 58 seconds north, and 71 degrees, 5 minutes, 53 seconds west according to the GPS.

We can also see how far we are from a reference point. Right now, we have Logan Airport in here. And Logan Airport is 3.58 nautical miles just about due east of us, 0.80 degrees. So in fact, if you look at it, you'll be able to see the tower of Logan Airport, off in the distance.

When I compared the GPS-measured coordinates of the Great Dome with the surveyed coordinates that Ken gave me, I found that the GPS located the Great Dome a few hundred feet north and west of Ken's location. And most of this difference was due to the selective availability effect. Now, there are ways we can correct for selective availability and other errors. And one of these is something called differential GPS.

Now, with differential GPS, what you do is you have another GPS receiver at a known surveyed location. And what it does is essentially calculates the current error due to selective availability. It then transmits this correction up to the operational GPS receiver so that you can locate position much more accurately. Basically, you're just compensating out the selective availability effect.

With differential GPS, it's possible to get your position to within a few feet if you're fairly close to the known surveyed receiver. Now, you can even do better. You can get accuracies as high as a few centimeters or a few millimeters if you use interferometric GPS techniques.

Now, we've talked about a lot of distance measuring techniques. And what I'd like to do now is go out and show you a simple example of a velocity measurement technique. Every time you drive a car, you actually see a velocity measurement on the speedometer in front of you. Now, my bike has an odometer, which actually works on the same principle.

Now, the way most odometers work is by counting the number of rotations of the wheel. In this case, on my bike here, I have a magnetics pickup. There's a small magnet attached to the spoke. And there's a magnetic sensor, here. Every time the magnet goes by the sensor, it creates a little voltage pulse. And that pulse is sent up this wire to the computer unit, here.

Now, the computer unit has a quartz clock in it. And the quartz clock, essentially, counts the number of pulses per second. If I know the circumference of the wheel, I can figure out what the velocity is. So for example, if I spin the wheel, you can see that there is an indication of pulses, here. And I get an indication of velocity.

I can also integrate the number of pulses, and I can get a total distance covered. In fact, on this ride, I've gone about 12.1 miles. I can accumulate that over time. So for example, the total number of miles I've ridden this bike is about 1,540.

Now, we can measure velocity using other techniques. For example, we can measure velocity by differentiating position measurements. So for example, if we take the GPS unit and differentiate position, we can get a velocity measurement.

At the 25 or 30 miles an hour I max out on my bike, there's not much risk I'm going to get pulled over for speeding. However, it's interesting to see how police actually measure velocity. Let's go take a look at that now.

We're out here on Memorial Drive in front of MIT, where I've enlisted the help of Sergeant Eric Anderson, from the Massachusetts State Police, to show us some of the different velocity-measurement techniques that are commonly used. We're going to look at both a Doppler radar technique and a LIDAR technique. This is a standard Doppler radar unit. And the way it works is by using the Doppler effect.

Now, what the Doppler effect is, is a shift in frequency caused by the relative motion of objects. And you're maybe familiar with this if you've ever heard a train whistle come at you. You'll hear the tone change as it comes at you and then goes away. You can almost hear it in some of these cars going by. The tone of the cars changes as it goes by.

Now, this same effect occurs with electromagnetic waves. And this unit uses a microwave with a wavelength of about 1 centimeter. And that's a frequency of about 24 gigahertz.

Now, what happens is the wave goes out from the gun to the approaching vehicle and is reflected off the approaching vehicle. The vehicle sees a Doppler shift. And the amount of the Doppler shift is proportional to the velocity of the car divided by the speed of light. So what the unit does is actually very carefully compares the outgoing frequency to the return frequency and then measures speed.

Now, there is a little bit of a problem with this unit, in that it's got a fairly wide beam. The beam width is about 12 degrees. So it sort of sprays out over the whole road. That's okay, because what it will do is it will lock onto the largest signal that's returning. That'll either be the closest vehicle or, in some cases, the biggest vehicle. If you have a bus or something like that, what will happen is you'll get a large radar return.

But it's a very good unit. There are some other units that are used that have actually tighter beam widths. And that's what the advantage of the laser unit. Let's take a look at that now.

ANDERSON: Trooper White is now utilizing the laser unit, which is a relatively recent speed-measuring technology for the law enforcement community. We really like it because it's officer-interactive. And the width of the beam is more specific. So we're actually targeting in on the specific vehicle without question.

HANSMAN: Yeah. The laser unit actually is-- even though it's more modern-- it's simpler in principle. What it does is it uses a time-of-flight technique and makes a range measurement to the vehicle. What you do is it sends out an infrared pulse, which goes out and bounces off the vehicle and comes back.

And by knowing the speed of light and the time it took the pulse to go out and come back, you can measure the distance to the vehicle. Then what you do is you measure the distance several times and get an estimate of the velocity of the vehicle.

You've got to be a little bit careful. You can't just do it with two pulses, because you might first get a hit on the front of the vehicle and then get one on the mirror or something like that. So that would cause an error in the measurement. And what these units do is make a lot of measurements-- about 360 a second-- to get an accurate measurement of the velocity.

This gun operates at a wavelength of 0.9 microns. And the reason it does that is for eye safety reasons. If you were to go to shorter, visible wavelengths, the light actually penetrates into the eye and could damage the retina. And at longer wavelengths, the energy is absorbed in the outer part of the eye and might damage the outer part. So this is actually the best frequency to use for eye safety reasons.

And as you said, the lasers have the advantage over the radars in the fact that they have a very tight beam width. This unit has a beam width of about 2/10 of a degree. So you can really focus on a specific vehicle, whereas the radar had a very wide beam width of 12 degrees.

I would now like to talk a little bit about the measurement of acceleration. Now, in principle, we can measure acceleration through the force it exerts. Since force is equal to mass times acceleration, if we have a known mass, we can, again, figure out the acceleration from force. And most accelerometers work on that principle.

You can see with this spring mass system, here, I have 100 gram mass. And the acceleration due to gravity shows me 100 grams on the scale. If I were to increase the acceleration-- if I were, basically, to accelerate the system up or let it come down, let it drop-- I would get a variation in the force that was read on the scale, here. In fact, if I were to drop the spring scale, the spring would return to zero since I'm now in freefall.

In fact, you can see that this creates a complication for us, on the surface of the Earth, if we want to measure acceleration for the purposes of figuring out what the subsequent velocity would be. Because on the surface of the Earth, even though this isn't moving, it feels that 1g acceleration down. The acceleration we feel on the Earth is a combination of the gravitational acceleration and something that we call the inertial acceleration. And in fact, that inertial acceleration is what you would integrate to get velocity.

Now, like I say, most accelerometers use this principle. However, most accelerometers aren't this crude. I have, here, an example of a piezoelectric accelerometer. And again, essentially, what it has is the same sort of thing on the inside. It's got a small proof mass or test mass inside. And it has a sensor. In this case it's a piezoelectric sensor.

Now that piezoelectric sensor sends a voltage out to this amplifier. And then that amplifier brings it up to a level which can be detected on this oscilloscope. Now, if I move the accelerometer up and down, you can see that the acceleration signal shows up on the scope, here.

Now, one problem with piezoelectric accelerometers is that they really only measure changes in acceleration. They're what we call AC devices. You need to use a different type of accelerometer if you are really interested in measuring the static, or DC, acceleration.

Another thing to notice is that this particular accelerometer is really only sensitive in one direction. And that's very common. Right now, its direction of sensitivity is up and down. Okay. So again, if I move it up and down, I get a pretty good signal. If I move it left and right, you can see that I don't get too much of a signal. In fact, any signal you do get is just due to the fact that I can't move it left and right perfectly.

Now, we talked a little bit about integrating acceleration to get velocity. And in fact, there's a navigation principle that's based on this. This is a model-- actually, it's an old model-- of an inertial navigation unit. And in principle, if you have three accelerometers, one measuring, say, north-- the yellow things, here, are the accelerometers-- one measuring east, and one measuring down, and you knew your starting position and starting velocity, you could integrate the acceleration to get velocity and integrate the velocity to get position.

So you would be able to navigate without ever having to make any outside measurements. And this is very desirable for applications such as submarines and some flight vehicles. And units like this are called inertial navigation systems.

Now, it isn't sufficient to just measure the acceleration, because you also have to be able to know which direction you were going. So these three red devices, here, are gyroscopes. And what they do is they measure any rotations that the vehicle has undergone.

Essentially, in an older system, such as this gimbal-based system, what would happen is if the platform rotated-- if the vehicle rotated-- the gimbals would adjust and keep the accelerometers oriented north, east, and down. Nowadays, it's more common to do that computationally. So basically, all the sensors would be fixed in what we call a strapdown inertial system.

Now, one thing to think about with inertial systems is that any errors in the sensors, either the gyros or the accelerometers, are integrated actually two times. So an error in acceleration would be integrated once, to result in an error in velocity. And that velocity error would then be integrated and result in an error in position. So errors in inertial systems tend to build. And it's necessary to periodically update both the alignment and the position of an inertial system to cancel out those errors.

We've talked about techniques for measuring distance, velocity, and acceleration, ranging from simple mechanical techniques to a variety of time-of-flight techniques. Since distance, velocity, and acceleration are related quantities, we can often use a technique to measure one to infer another. However, it's important to remember that distance, velocity, and acceleration are vector quantities. So it's important to consider both the magnitude and direction when making a measurement.