I’m currently reading Richard Conniff’s Natural History of the Rich (which, by the way, is well-written and really entertaining).
In it, he mentions a Muslim prince who had a 747 with a prayer chamber that was gyroscopically controlled to always be oriented towards Mecca. Could someone explain to me how that might work? I am not a science type, so take it slow.
Here’s what I do understand, I think. Gyroscopes are free-moving within their frame, right? So I could see how you could use one to keep a chamber oriented toward magnetic north, by attaching a big honking magnet towards one side. (Please, be gentle if you have to disabuse me of this notion.)
If you wanted to keep the chamber always oriented towards a particular direction other than north, I’m guessing that could be done electronically in some way (though I’m starting to get confused here, since if you’re controlling the orientation, aren’t you interfering with the free-floatingness of the gyroscope?).
It’s at contemplating a fixed orientation towards a single global point that my brain starts to sizzle and smoke. Orientation towards Mecca isn’t just about facing east (in the U.S.; this obviously varies by where you are) once you’re moving. I’m imagining a plane flying west to east across, say, Russia. Mecca starts out southeast of you, then it’s south, then southwest, of you. Is is just a matter of sophisticated programming (and, again, please be gentle if it’s not terribly sophisticated programming) to maintain the orientation to the fixed spot?
I laid all this out so you could see what I am and am not getting, kind of, here. I think my actual questions are two:
Is there a conflict between the gyroscopeness of the gyroscope and using it to keep something oriented in a particular direction? Why or why not?
If there’s no conflict, is it significantly more complicated to use a gyroscope to keep something oriented to a fixed point, rather than in a particular direction?
The way I understand gyroscopes is that they take advantage of the tendency of moving objects to remain moving (and resist changes in course). Measuring the resistance should allow you to calculate how you have changed in orientation, allowing very exact measurements of your facing. You know how your facing has changed but this does not really correspond to any global constant; you just know you have turned 3 degrees “thataway” from your starting orientation.
In order to keep something pointed toward a particular destination, you would want to have a gyroscope and some other instruments such as a speedometer and a watch. You would have to calculate your new position constantly, and then the correct angle toward your target. What the system you described probably does is update its position using GPS, and then uses the gyroscopes to orient the chamber based on that information.
(Oh, and the Earths magnetic field is almost certainly too weak to heave the chamber about no matter how large the magnet, and even less likely with a gyroscope.)
In the areas that aren’t too far north, being linked to the north pole is the same as being oriented east. It it just depends on which part of the room you mark. Since east is ninety degrees from north, just orient the room north, and point a big honking arrow 90 degrees from that.
The principle involved is the conservation of angular momentum. It’s the same thing that makes a bicycle stable when it’s moving, and unstable when it’s standing still.
Take a heavy weight, point it in a specific direction, then spin it. Once spinning, it will resist being rotated. So put it on ‘gymbals’ with good ball bearings so that it can freely rotate within the aircraft, and then no matter which direction the aircraft turns the gyroscope will remain pointed in its original direction.
BTW, this is how direction and attitude indicators work in the cockpit. There are little gyroscopes inside that are spun to high speeds either by air pressure or electricity. The pilot uses a knob to turn the gyroscope so the needle is pointing in the right direction, and after that the gyro will remain fixed as the airplane turns.
There are some gotchas. one is ‘precession’ - if you try to apply a force to a gyroscope, it will react at a 90 degree angle to the implied force because of the rotation. That’s why you have to lean into a turn on a motorcycle or bicycle. In a gymballed gyro, friction from the bearings causes the gyroscope to slowly precess. If you don’t correct for it, you may find yourself eventually praying to New Jersey instead of Mecca.
If the author himself wasn’t a science type, then his phrase “gyroscopically controlled” was wrong. Hooking the chamber to a big gyroscope is not the way to do this.
There is a device called an “inertial guidance system” which is used to track location and orientation of aircraft, missles, etc. There is also a device called a gyrocompass (a compass not based on magnetism and which is immune to magnetic fluxuations.) Inertial guidance systems contain gyrocompasses.
Years ago, before GPS systems, the best way to keep a prayer chamber oriented towards Mecca would be to use an inertial guidance system to keep track of the current location and orientation of the aircraft. Since the location of Mecca is well known, a simple computer could then do the vector math and then run some motors which turn the prayer chamber in the appropriate direction. The gyroscopes don’t do it directly, but they play an essential role by acting as a compass.
Today you’d use a GPS receiver, a computer, and some motors under the prayer chamber.
Okay, I have no idea whether I’m getting this or not.
Phage – so the free-floatingness of the gyroscope is about its ability to reorient, and that reorientation is probably based on information from GPS. To maintain orientation to a direction, it would be about maintaining a constant orientation to a single axis (e.g., if you want to stay pointing east, the system would have to correct when your position changed to one at some measurable difference from the east-west axis).
With orientation to a fixed point, you’d have to have to orient to two axes, N-S and E-W, with those two axes crossing at your target point (in this case, Mecca). GPS would give you info about your degree-difference from that point and then your room-movers (whatever the hell that technology is) would correct your position. So, if I were five degrees to the west off the N-S axis, the room would correct me by creating difference of five degrees to the east. Am I in the ballpark here?
Sam Stone – It’s been well over a quarter of a century since I took Bonehead Physics – I’ll be honest with you, if you open the mental cupboard in my brain marked “the conservation of angular momentum,” a couple of mangy looking moths will come flappin’ out.
Specifically – I’m not sure what the difference is between “spinning” and “rotating,” and I’m not sure how you “point” the object. What kind of object are we imagining here? How do you point it? How do you spin and/or rotate it? and what does any of this have to do with my sheik’s jumbo jet?
Twickster, you may be seeing this as a bit more complicated than it really is. bbeaty has it right.
To point toward Mecca, you need to know where Mecca is (easy to determine) and where you are (see below). Position is often expressed in terms of latitude and longitude. If you know Mecca’s lat/lon and your own, it’s really simple to calculate both its distance and direction from you. When you know its direction and your heading, it’s no big problem to point the “prayer room” toward it.
Keeping track of their position has long been popular with sailors and aviators – even those who don’t care about pointing toward Mecca. In the days before GPS (and to a considerable extent still today) those who could afford it (e.g. 747 owners) often used an inertial navigation system to help with this job. The principle is that if you start at a know place and keep track of your every movement, you know where you’ve got to. Gyros are important in an inertial navigation system – they let the system keep track of changes in direction. Nowadays, with GPS, you can get much the same information for much less trouble and money.
So when the author talks about a “gyroscopically controlled prayer room” he’s almost certainly indulging in bit of hyperbole. The prayer room was under the control of a device that needed to know the plane’s position, and the plane used a gyro (and some other things) to keep track of its position.
Boy, that would be a completely unprecedented development!
So, in other words, Xema, you’re saying that the older, more primitive system used gyros to keep track of each movement between points A and B – whereas now, using GPS, they don’t bother to actually trace that path (and I’m having a horrifying “Family Circus” mental thing here), but just check with the satellite at Point A and then again at Point B.
Oh, come on, it’s that simple? Where’s the fun in that?
It might be slightly more accurate to say that inertial navigation systems keep track of every small movement and do a continuous calculcation of the effect these have on position. They use gyros, accelerometers and other stuff.
And it isn’t really right to imply that inertial navigation is primitive – it’s extremely sophisticated. It is true that you can now get similar performance for a heck of a lot less money.
Sort of. GPS receivers typically calculate your position every couple of seconds. Unlike inertial navigation, they don’t have to keep track of your movement – they get a complete lat/lon position each time.
Here’s one way to say it:
Inertial nav: Uses prior position and history of movement to calculate current position. “Let’s see: 32 minutes ago we started on Runway 22 at JFK. We took off, turned west, climbed to 26,000’, accelerated to 512 mph – all of which puts us right HERE [displays current lat/lon].”
GPS: Listens to signals from satellies and calculates lat/lon from them; doesn’t need to keep history, but often does so. “Signals from the 7 satellites I’m now receiving say we are HERE [displays current lat/lon]. Would you like to know how far we’ve come since takeoff? Our average speed?”
Lots of folks use the term “GPS” pretty casually to refer to the satellites, or maybe the broadcast radio signals, or maybe the receiver, or maybe the data displayed on their particular model of GPS device. Gotta be careful about loose terminology interfering with clear understanding.
A GPS satellite continuously broadcasts an encoded time value called a GPS signal.
A GPS receiver receives signals from several satellites and converts that into an instantaneous lat/long & altitude (ie 3-D position) and exact time. That’s all a GPS receiver can do. There’s one of those embedded in your cellphone.
By taking multiple readings at a fixed interval (say every second), a GPS navigation system, can compute the change in lat/long over the interval and thereby derive a direction of motion and a rate of motion. In other words, a velocity vector. That equates to a ground track and speed. Most handheld GPS navigators can do this, as can units sold for use on boats, cars and aircraft. Simple units sold for hiking often cannot.
As a practical matter, the nav systems in modern jets use several different sensors and GPS is just one of the inputs to ariave a complete blended and filtered answer to the base questions “where are we?”, “what direction are we going?” and “how fast are we going?.”
Those answers are then used to derive lots of other facts, such as the direction from here to Mecca, expected time to get there, expected fuel burn, etc.,etc.
There are layers and layers of complexity and details once you scratch the surface. In most installations GPS is NOT used as a primary source for direction information; the delta lat/long signal is too noisy. A gyrocompass provides the current direction information, and long-term filtered GPS data is used to trim the raw gyrocompass values.
Well, since the question has been answered, and I find myself unable to supply a little bit of aviation knowledge for others now, I feel like a small hijack:
What if the airplane was in the exact opposite place on earth from Mecca? So, Mecca is 21 degrees 29 minutes north, 39 degrees 45 minutes east. If the airplane is at 21.29 south, 39.45 west, what direction does he have to face to pray properly? Does he just pick a direction, or does he have to point straight down?
Apologies if the hijack is not appreciated. This is the kind of question I think of when I’ve been drinking.
Probably the program would have a default built in, round a number or something, and just pick a direction to face (or not change orientation). I think that he would be justified to pray in any old direction at that point. I don’t think that people are required to pray “down” when they are near the other side of the world.
I thought a GPS receiver measures instantaneous velocity based on Doppler shift? Otherwise the speed and bearing displayed by my handheld GPS receiver seems too accurate. It displays believable velocity readings even before I’ve walked 7 meters, which is the stated accuracy of the receiver.
Well, different GPS receivers can have different sampling intervals. For ones used on airplanes a reading once per second is accurate enough because of the large speeds normally involved. The more often you sample the GPS signal the finer your positioning can be.
This site discusses GPS receivers being used as seismometers with a 10-20 Hz sampling rate. (Warning: PDF).
If your handheld GPS samples at 2 Hz, how many samples will it have by the time you’ve walked 7 meters? If walking at 1 meter/sec by the time you’ve covered 2 meters the receiver has 4 samples, and by the time you’ve covered 7 meters it has 14 samples. Either one is enough to generate a velocity vector.
The stated accuracy of GPS navigation systems has to do with pinning down your location while stationary. With no movement your receiver can pinpoint your location on the Earth to within 7 meters (If it’s stated as CEP or Circular Error Probable it means that 50% of the time you will be within a 7-meter circle of where the unit thinks it is). Start moving, though, and the extremely accurate signals from the satellites start to shift and the unit can resolve your velocity. How accurately it resolves this is dependent upon the software in the navigation unit interpreting the data from the receiver, and it sounds like you’ve got a fairly accurate unit. You might want to tinker around in your GPS unit’s menu and see if there is an option for “sampling rate” or something similar. Try varying this and see how your velocity accuracy varies.
Or an even better question: since the plane is moving, does the room just spin around and do a 180 when the plane crosses the line on the globe exactly 180 degrees from mecca and suddenly the holy city is closer from the west than the east?
