Well one funambulist doesn’t need to be with another to walk on a “fun”…oops… a cable.
There can be reasons that you can’t have the two vehicles balancing each other on the funicular railway, but the initial costs and running costs are reduced if you can. The most critical feature is that the vehicle is towed by a cable.
If the train has a gear type wheel , known as a pinion, for ensuring traction on the steep section of railway, its called a rack railway, the pinion engages the rack … the similar gear and linear toothed strip in a road vehicle used for steering is called rack and pinion, even though its the rack which moves to actuate steering.
Some of my customers expect horizontal distances in nautical miles and vertical distances in kilofeet. I do everything in meters, of course, and do a unit conversion at the end; 1 nmi = 1852 m, 1 kft = 304.8 m. Fortunately, there’s no slopes or volumes needed.
You could always use Topographic slope. Rise per 66 ft.
When I’m designing a road I could use the geometry I learned in school. But the geometry I learned in school can approach a triangle from any side or angle. Mountains aren’t built like that. If I set my triangle so the 90º is always in the same location and I’m only finding the one angle I would only need to use the tangent function. Deg=Tan-1(Opp/Adj). If I set my adjacent side to always be 100 the only data I need is the opposite side. If the only data that I need is the vertical change per 100 ft there is no point in running it through the tangent function to get degrees.
That’s my non-mathematician proof from a guy who uses clinometers to design and build basic roads.
Apropos of nothing but I was on the new Stoos funicular during my wedding/honeymoon. Pretty disorienting ride, but unfortunately the weather didn’t cooperate to allow the hike so the trip was for naught.
It makes plenty of sense for the car to have a counterweight. But the counterweight doesn’t necessarily have to be another car. If you don’t have enough width for two cars to pass each other, not even in the middle, then you could use a lead slab that passes underneath the single car.
Well that’s just aviation. Yet more accidents of history. Nothing wrong with nautical miles however.
If the Earth were a perfect sphere the conversion from nautical miles to kilometres would be exactly 0.54 = \frac{9 \times 6}{100}
But it isn’t quite, which is a small price to pay for the sun to come up in the morning.
Nautical miles and kilofeet work together quite well in aviation. Pilots are very interested in paying attention to their vertical speed (changes in altitude). Glider pilots in particular are very interested in their rise or sink per thousand feet.
A nautical mile is approximately 6076 feet. For quick mental approximations, that’s close enough to 6000 feet. If you know the glide ratio of your glider (e.g., 30-to-1) you can easily estimate the horizontal distance you can cover per 1000 feet of lost altitude.
Example: You are 5000 feet above ground level, and about 12 nautical miles from the nearest airport. Your glider, Grob G-103, has a glide ratio of 36-to-1, but to give yourself a good margin of safety, you assume half that, 18-to-1, and work with that. (These are real-life realistic numbers.) Assuming still air, can you make it the 12 miles to the airport? This type of problem is real easy to work with in horizontal nautical miles and vertical kilofeet. (ETA: Note, you want to be at least 1000 feet AGL when you reach the airport.)
It’s for real that a nautical mile is approximately 6000 feet. And the G-103 glider really has a glide ratio of 36-to-1, for which 18-to-1 is commonly used for a big margin of safety. Those are the numbers that make it easy to do mentally. The 12 mile distance was an arbitrary choice, but that doesn’t much affect the ease of doing the computation. (You figure how far you can go with each 1000-foot loss of altitude, and multiply that by your altitude in kilofeet [less 1000 because you want to still have 1000 feet when you reach the airport] and then see if that is more or less than the distance you hope to go.)
Whatever the glide ratio is (even if not a multiple of 6), that is fairly constant for a given glider, so you can figure in advance how far you can go per 1000 feet of altitude and keep that in mind (suitably rounded). Then, at any moment, just look at your altimeter and see how many kilofeet you have, and quickly figure how far you can go.
Use metric and you have no conversion factors involved at all. Sort of why we use it everywhere else. But traditional navigation methods work nicely in nautical miles, and changing from feet to metres for altitude would have been a good way of causing no end of accidents.
The difference between nautical miles and kilometers I alluded to above comes down to whether you like to have nice divisors in your unit base. Metric is a pain because we decided aeons ago that we would use base 10 for arithmetic. But there is no right answer. Base 12 is lovely, and the Babylonians saw the merit of 60. Which is the core of the difference between nautical miles and kilometers, and why we still like to by things buy the dozen. When integers are involved base 12 beats base 10 for utility.
One is reminded of the Air Inter Airbus 320 accident where the auto pilot’s rate of descent was set in either Vertical Speed Mode, in 100s of feet per minute, or in Flight Path Angle Mode, set in decimal degrees. So the display would read 33 (3300 f/min) or 3.3 (3.3 degrees) depending on mode. The presence of the decimal point being the only way to tell what mode the autopilot setting was in, and thus the actual set descent rate. At the speed of the aircraft the difference was about 10 times. 87 of the 96 people on board were killed.
But if you’re figuring that in advance, then you can use any units at all. To illustrate, suppose that we instead measured altitude in hectameters, and horizontal distance in leagues, and suppose that our glider has a glide ratio of 29:1. That means that for every hectameter I decend, I’ll glide 29 hectameters horizontally. 2900 meters is 0.52 leagues, so round that to half a league, and call it a quarter league for that safety factor of 2. So now I can just take my altitude in hectameters, and divide it by 4 to know how many leagues I can glide to reach the airport.
I just chose those units and that glide ratio to be as inconvenient as possible, and it still came out to where I could do the relevant calculations easily. And I could likewise come up with easy calculations for any other combination of units and glide ratios.
Point taken. Of course, it’s always useful to use the same units that everyone else, including published documents, is using.
You’re also correct that weird numbers can be rounded to convenient numbers. That 2-fold safety factor gives a lot of room for error. For example, another popular glider has a glide ratio of 22-to-1, half of which is 11-to-1. Rounding this to 12-to-1 (in the “unsafe” direction, but with that 2-fold fudge factor, big deal), gives a convenient glide distance of 2 nautical miles per 1000 feet of altitude.
Knots and kilofeet aren’t going anywhere any time soon in aviation, but this calculation will always be easier in metric just because you don’t have to have a unit conversion factor. 12:1 glide ratio converts to 12000 meters horizontally for every 1000 meters elevation.
Of course it’s more important that everyone be on the same page than it is to avoid unit conversions, and so knots and kilofeet it will remain.
Yeah, it’s often overlooked, but this is the single most important thing about a system of units.
Which is, of course, yet another point against the “customary” units, because you’re never sure if anyone else is using the same pints or inches or pounds or whatever as you are.
Well it also converts to 12 furlongs horizontally for every vertical furlong.
Using nautical miles for horizontal distances and feet (or kilofeet) for vertical distances has another advantage: While the airspeed indicator is marked in knots (nautical miles per hour), at least in European or other non-American aircraft, the vertical speed indicator (often called a variometer in gliders) is marked from 0 to 10 in units of 100 feet per minute. This very conveniently works out to be ≈ 1 knot. So the variometer also shows vertical speed in knots, the same units as the ASI. That makes it very convenient to figure your glide slope at any moment.
Absolutely 106% true! And as we all know so well, the great thing about standards is that there are so many to choose from!
