## Hill Steepness Rating

snave_biker
Posts: 1
Joined: Tue Jul 10, 2007 07:09 am

### Hill Steepness Rating

Hi,
I sometimes read about Hill steepness and the difficulty being mentioned as 1 in 4 or 1 in 6, what exactly does this mean and what is the harshest gradient?

Johnpwr
Posts: 47
Joined: Wed Jan 24, 2007 14:46 pm
Its the ratio of distance travelled upwards compared to the distance travelled forwards, so a 1 in 4 gradient is going up 1 metre for every 4 metres forwards.

1 in 4 is definitely into 'get off and walk' territory unless it's very short

You also see these as percentage gradients, so 1 in 4 is a 25% gradient while 1 in 7 is 14%

ColinJ
Posts: 2179
Joined: Mon Sep 05, 2005 14:23 pm

### Re: Hill Steepness Rating

snave_biker wrote:Hi,
I sometimes read about Hill steepness and the difficulty being mentioned as 1 in 4 or 1 in 6, what exactly does this mean and what is the harshest gradient?

The harshest possible gradient is actually a vertical cliff!

Mathematically speaking, I think the way we talk about gradient is wrong because it should be calculated as (vertical height gain) divided by (horizontal distance travelled). It's much more practical to measure the distance along a road rather than the distance into a hillside so that gets used instead. For moderate hills, the error is pretty small. Even the figures given for steep hills aren't too far out. What we call a '1 in 4' should really be a '1 in 3,873...' (by Pythagoras' Therorem), an error of just over 3%. The error gets huge as a slope approaches cliff-like gradients. Using the conventional way of stating the gradient, a cliff would be a 1 in 1 (100%). Actually it would be a 1 in 0 - infinitely steep.

The steepest road gradients would be between about 1 in 2.5 and 1 in 3, but they are very rare because they are impractical. Steeper than that and you wouldn't be able to get any sort of conventional vehicle up them (you'd be in cable car and funicular railway territory). As for going down them...

By the way, to see pictures of some really steep hills, follow the links in this thread

Raph
Posts: 240
Joined: Sat Nov 20, 2004 00:01 am
The way I've always understood it is that a vertical cliff would be 1:0, and 1:1 is 45deg. e.g. a 1:4 is one unit vertically upwards and four units horizontally along. I often try and estimate a horizontal line from the top of my head to a point where the ground will come up to intersect it and estimate how many of me I could lie end to end in a straight horizontal line - admittedly an almost pointless exercise since estimating an accruate horizontal when you're on a steep slope is impossible with no references, and imagining yourself lying down in mid-air end-to-end lots of times is similarly hard! Also I'm very slightly taller on the bike than off since I can't quite reach the ground from the saddle... Doesn't stop me passing the time while winching endlessly up a steep hill though.

It doesn't seem a wrong way of thinking about it, as long as you've got it right in your mind that 1:1 isn't vertical (never occurred to me it would be anyway). At gradients approaching 1:4, it gets a bit academic anyway, you need all your strength and a fairly un-macho gear to stay on the bike at all. My best effort ever was a longish 1:4 in the Dales on a 42 front 21 rear (54") with tons of luggage. I didn't know it was coming up so I couldn't get wound up about it and just got on with it. A few weeks later on a different bike, unladen, I had a bottom gear of 63" (18 rear) and couldn't manage a 1:5.

I've found cars sometimes unable to get up 1:4s - I had to take a van over hardknott pass once, and kept skidding on the steepest bits. My passenger had to go and sit over the back axle to get a bit more grip to stop it skidding. I dread to think how I'd got up there with front wheel drive. Even on a bike I've had back wheel spinning going over wrynose and hardknott.

Cajun
Posts: 1029
Joined: Thu May 08, 2003 20:21 pm
Calculator for Slope & Distance Equation:
http://www.1728.com/distance.htm