# How can an incline be 106%? **URL:** \ **Category:** Factual Questions\ **Created:** [March 6, 2022, 4:33pm UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571 "2022-03-06T16:33:04Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [March 7, 2022, 7:13pm UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/21 "2022-03-07T19:13:31Z")
Beat me to it. The article states that it is not technically a funicular (though it looks like other funiculars I’ve been on, minus the corresponding second car, which partly defines the funicular.) ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [March 7, 2022, 7:53pm UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/22 "2022-03-07T19:53:23Z")
> [@kenobi\_65](#): > > Pictures I can find of it online all seem to suggest it’s only a single track, so I suspect it’s not a funicular railway in the traditional sense, and is more like an inclined plane railway. Single track is pretty normal for a funicular. The only place you need double track is at the midway point. Here’s one in Japan, with the video cued to the just before the two cars encounter each other at the midpoint: [![](https://img.youtube.com/vi/VxWdZhQ-ZOc/maxresdefault.jpg "比叡山鉄道線 ケーブル坂本駅坂本ケーブル Sakamoto Cable, Hieizan Railway, The Longest Funicular Line in Japan [4K]") ](https://www.youtube.com/watch?v=VxWdZhQ-ZOc&t=332) That said, I now see that the Gelmer Funicular, despite its name, is not a true funicular. From your Wikipedia link: > It is technically not a [funicular](https://en.wikipedia.org/wiki/Funicular), which has two cars that counterbalance each other, but is propelled by a [winch](https://en.wikipedia.org/wiki/Winch). ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 8, 2022, 12:07am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/23 "2022-03-08T00:07:39Z")
> [@Pleonast](#): > > There’s “fraction of a whole, expressed with a denominator of one hundred” Or, simply the numerator of a fraction with a denominator of one hundred. At least that’s how I’ve always read them. 106% is a perfect synonym for 1.06, no more and no less. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 8, 2022, 12:12am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/24 "2022-03-08T00:12:26Z")
> [@CookingWithGas](#): > > I guess it doesn’t bother civil engineers. Think about it in practical terms instead. It’s difficult for a civil engineer to measure the angle that a road makes with the horizontal, because in practice roads are kinda wavy and using a plumb bob in one location isn’t going to give you a great figure. But what is easy is to measure out 100 feet horizontally and figure out the rise over that distance. A 4 foot rise means a 4% grade. A 106 foot rise would be 106%. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 8, 2022, 12:21am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/25 "2022-03-08T00:21:52Z")
And then there are grads, an angle measure each of which is equal to 1/100 of a right angle, and which I believe exists nowhere except on some TI calculators. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [March 8, 2022, 1:25am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/26 "2022-03-08T01:25:15Z")
Depends on country. Some military forces still use grads for artillery elevation angle.\* It does creep into some corners of arcane engineering as well. Some HP calculators did grads too. \*And other awful units too. Kiloyards anyone? ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 8, 2022, 1:28am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/27 "2022-03-08T01:28:17Z")
> [@Francis\_Vaughan](#): > > Some HP calculators did grads too Just checked, and my 48GX (ok, the emulator that I run on my phone… but I still have the physical one) supports degrees, rads, and grads. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [March 8, 2022, 1:37am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/28 "2022-03-08T01:37:42Z")
Ha! I still have my HP-25 but use it’s emulator on my phone. My fingers know exactly where to go after all these years so it is most efficient for me. I suspect one can date us all by these models. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 8, 2022, 1:37am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/29 "2022-03-08T01:37:58Z")
Huh, so it does. I guess I never noticed because it’s tougher to accidentally put an HP48 into grad mode than it is for a TI30. ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [March 8, 2022, 1:43am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/30 "2022-03-08T01:43:44Z")
Watching snowboarding and freestyle/slopestyle skiing in the Winter Olympics recently, I thought to myself that it sure would be easier if those athletes expressed it in grads instead of degrees. A 1440? How many is that? ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [March 8, 2022, 1:49am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/31 "2022-03-08T01:49:30Z")
> [@CurtC](#): > > 1440? How many is that? 25.137 radians. Easy. 😝 ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [March 8, 2022, 1:55am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/32 "2022-03-08T01:55:04Z")
> [@Francis\_Vaughan](#): > > 25.137 radians. Easy. I hadn’t really thought of that, but actually 25 radians “feels” like about four revolutions to me, whereas 1440 degrees I can’t parse until I do the arithmetic. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [March 8, 2022, 1:59am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/33 "2022-03-08T01:59:43Z")
It occurs to me that a much more friendly unit would actually be radians. But with \pi as an included multiplier. So a 1440 should be an “8 pi” jump. Your average viewer would not take long to get the idea that “pi” was a 180 degree turn. Even the dumb commentators could cope with that. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 8, 2022, 2:05am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/34 "2022-03-08T02:05:22Z")
> [@Francis\_Vaughan](#): > > It occurs to me that a much more friendly unit would actually be radians. But with \pi π\pi as an included multiplier. Or tau. 4 \tau radians. Done. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [March 8, 2022, 2:10am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/35 "2022-03-08T02:10:06Z")
> [@Dr.Strangelove](#): > > Or tau. 4 \tau radians. Done I was thinking about \tau but lots of jumps can involve half turns so leaving it as \pi keeps it an integer. Bringing up the \pi versus \tau war is probably not going to help here. 😜 ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [March 8, 2022, 2:18am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/36 "2022-03-08T02:18:31Z")
Sometimes it makes more sense to include the 1 \over 2 factor, though. \frac{1}{2}\tau r^2 for the area of a circle is arguably clearer (though the visual similarity between \tau and r isn’t great), because that 1 \over 2 factor comes from the solution to the integral. It then looks analogous to formulas like \frac{1}{2} m v^2 ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [March 8, 2022, 2:40am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/37 "2022-03-08T02:40:54Z")
I agree. But that horse has bolted. Such is life. The point about the integral is well made. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 8, 2022, 2:44am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/38 "2022-03-08T02:44:21Z")
Or, if you use the usual geometric argument, it’s the same \frac{1}{2} as in the triangle area formula. Which is also, of course, the same one as from the integral of x. ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [March 8, 2022, 3:36am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/39 "2022-03-08T03:36:15Z")
> [@Francis\_Vaughan](#): > > Even the dumb commentators could cope with that. In ice skating they talk about triples and quads. Seems like _everybody_ can cope with that. Why talk about degrees? ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [March 8, 2022, 5:46am UTC](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571/40 "2022-03-08T05:46:06Z")
So if a mathematician walks into a bakery and orders a whole pie, he actually gets 2π radians of pie. If the announcers and commentators think like that, they will get really confused. [Previous page](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571.md?page=1) [Next page](https://boards.straightdope.com/t/how-can-an-incline-be-106/960571.md?page=3)