Use of Slopes in Design - Is there a mathematical calculation I can apply?

[MCirba]

All,

I'm not very good at Geometry and forget most of the calcs I learned in 10th grade.   

Let's say I'm trying to figure out a hole design and it requires a 70 foot elevation change from the tee to the landing area.   Approximately how far would a golfer need to drive a ball on level ground to reach a target 300 yards away given the 70 feet of elevation change?   

Let's assume I'm about 150 feet above sea level and all other things being equal.   

Is there a sliding scale formula I can use to approximate if the elevation change was say, 40 feet instead?   I'm thinking architects looking to place hazards or determine carries in their landing zones need to do this type of thing routinely, and am hoping to learn.

Thanks in advance for your assistance!

[Matt Frey, PGA]

Rangefinders with inclinometers make it easy, however, in this video, Trackman correctly states that everything depends on the ball trajectory: https://youtu.be/te24Dh26nck


There are some (very) basic formulas in that video.

[Jason Topp]

I have always assumed that 45 degrees is a reasonable approximation of the descent angle of a golf shot. 

If that is correct, 1 yard up or down will equal 1 yard of carry.  The slope of the landing spot will have a very significant impact on how much the ball rolls assuming the conditions are firm enough to allow roll. 

[Tom_Doak]

I have always assumed that 45 degrees is a reasonable approximation of the descent angle of a golf shot. 

If that is correct, 1 yard up or down will equal 1 yard of carry.  The slope of the landing spot will have a very significant impact on how much the ball rolls assuming the conditions are firm enough to allow roll.

That's the formula I have generally seen caddies use.  I always thought it was a bit more than that, for my game ... that 30 feet uphill meant more than a one-club difference.  But my trajectory is not the same as that of a really strong player.

[MCirba]

Thanks guys, that's very helpful.

[Kyle Harris]

That green should be out of harm's way. 

"I didn't think it was a problem; I just wanted them to analyze it."
 

[MCirba]

Kyle,


I thought you might like to play.


What about a green 300 yards from a tee up a 70 foot elevation change?

[Jason Topp]

That green should be out of harm's way. 

"I didn't think it was a problem; I just wanted them to analyze it."

Me too.  I also do a poor job of estimating how far uphill or downhill a shot actually is.  I have at times checked top maps and been surprised.

[Jeff_Brauer]

I have always used the yard for yard rule of thumb, too.  I think Forrest had something his book pointing out that we aren't crazy...uphill and into wind hurt us a bit more than downhill and downwind help us.

[Thomas Dai]

There's bound to be a mathematical model taking into consideration all kinds of things like ball speed, loft, spin, humidity, temperature, altitude etc.
Simulators/trackman etc are bound to have various general assumptions built into them. It would be interesting to know what the assumptions are and how they were arrived at.
I suspect going downhill has less effect than going uphill, just a suspicion though. And then there's other factors like wind and rain.
Generally I've always worked on the one foot of elevation is one yard in clubbing but each to their own.
There's always this - https://m.youtube.com/watch?v=HNMtt94x1Y0 - 😄

Atb

[MCirba]

Let me see if I have this right. Are we saying hitting a driver to a 60-foot uphill target I would expect to lose about 20 yards of carry?

[Pete_Pittock]

Tom Doak,
Is there a formula for tee shots over ridges. The two most 'gulps' I've had on golf courses were 9 at Pacific Dunes and 18 at Dismal River.


Grassing could alter the slope formula. At Sagebrush I could hit driver off the deck considerably further than off the tee (8,16) with the firm fescue maintenance meld.

[Jason Topp]

Let me see if I have this right. Are we saying hitting a driver to a 60-foot uphill target I would expect to lose about 20 yards of carry?

That is what I meant

[jeffwarne]

uphill and into wind hurt us a bit more than downhill and downwind help us.

Uphill really hurts the average player/lower speed player who often fails to factor in the effect of hitting an iron off an upslope artificially lofts it more than they expect.
The wind is actually LESS of a factor uphill(for the better player) as the hill itself mitigates the effect of the wind by blocking the wind until the ball gets higher than the top of the hill.


Downhill into the wind can play quite long if the player can't control his trajectory.


For the most part, average players simply don't account for gravity nearly enough on all shots

[Tom_Doak]

uphill and into wind hurt us a bit more than downhill and downwind help us.

That is the nature of physics ... the golf ball travels in a roughly parabolic curve, due to gravity, with its ascent becoming steeper as you go.  If you visualize a parabolic curve going down below the normal zero line, it's going to be very steep, and you're not gaining much distance at all.  If you move the point of return [ground level] high above the point of takeoff, you will lose a lot of distance.  If the target is 30 yards above the fairway, a lot of people are never going to get there in one shot, because they don't hit it that high!


But ... the longer it's in the air, the longer it keeps hooking or slicing!  That is why I'm not a big fan of steep downhill shots as a part of design.

[MCirba]

Wow...some of this stuff should have been more self evident to me but I really appreciate having it spelled out.


Let me ask for a practical application.  If I were building a driving range with a gradual uphill slope reaching 70 feet above the tee at 300 yards do folks think a tall fence would be needed at the end of it?

[Thomas Dai]

But ... the longer it's in the air, the longer it keeps hooking or slicing!  That is why I'm not a big fan of steep downhill shots as a part of design.

The time the ball is in the air and what can happen to it is also a reason why very short par-3's in windy locations can be challenging to the longer hitter who isn't able to control the flight of his short irons and wedges. High shots with spin also plug when landing in bunkers.

Atb

[Jeff_Brauer]

Wow...some of this stuff should have been more self evident to me but I really appreciate having it spelled out.


Let me ask for a practical application.  If I were building a driving range with a gradual uphill slope reaching 70 feet above the tee at 300 yards the folks think a tall fence would be needed at the end of it?

Mike, the shot traces a parabola, with its apex at 70% of flight.  For 300 yard drives, shot height can reach 130 feet or so.  Most golfers hit maybe 90 feet high.  So, somewhere around 200 yards out left and right would be where the highest net would be needed, perhaps not the end.


I'll answer your next logical question - typical max angle dispersion off the tee is 17 deg. left and 24 deg. right........that catches maybe 99% of shots.  Try to arrange your flight patterns accordingly, and figure the netting on the right side especially for 180-220 shots to be the max of 90 if  under that.

[Mike_Young]

Wow...some of this stuff should have been more self evident to me but I really appreciate having it spelled out.


Let me ask for a practical application.  If I were building a driving range with a gradual uphill slope reaching 70 feet above the tee at 300 yards the folks think a tall fence would be needed at the end of it?

You will not need a fence....

[Bob Harris]

Mike,
For course rating purposes, the USGA rating formula increases/decreases the effective playing length by 2.3 yards for each 10 feet of elevation change.


Bob

[MCirba]

Thanks so much Jeff and Mike.  Really helpful info.  Thanks also Bob for some interesting comparative information.

[Kyle Harris]

For the most part, average players simply don't account for gravity nearly enough on all shots

I feel like this is a punchline.

[Steve Lang]

   Why did the engineer cross the road?




Mike, IF you want to get a little quantitative you may want to check out things at Dave Tutelman's website:


http://www.tutelman.com/golf/ballflight/CompareTrajectoryPrograms.php


get a trajectory program, like Trajectoware... then again, maybe not