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I wrote parts 1 and 2 in parallel hoping to make part 1 more readable by sticking to words and ideas and putting diagrams and calculations in part 2. I didn't think many people would feel moved to read part 2 so in order to make part 1 stand on its own there is some copy and paste of words from part 2 to part 1.
Dealing with Uppers part 2 - Tables - version 9,746,211 2004-2-2
------------------------------------------------------- --------
OK - Where Did Those Tables Come From?
--------------------------------------
Let's start with the overall picture:
UPPERS ------ > <------------------------------------- AIRPLANE
__X __X ____X ____X __X __X
/ / / / / /
| | | | | |
\ \ | | \ \
\ \ | | \ \
\ \ | | \ \
\ \ | | \ \
\ \ | | \ \
| | | | | |
__/ \__ __/ \__ | | | |
| | | |
__/ \__ __/ \__ __/ \__ __/ \__
AFF's, Tandems Fast Falling Slow Falling
High Pullers Freeflyers Boards, RW
# # # # # # # GROUND # # # # # # # # TARGET # # # # # # # # # # # GROUND # # #
We see that the fast fallers get more forward throw and less freefall
drift than the slow fallers, but with similar tracking and canopy motion
at the bottom, so we only need to figure out how to separate two adjacent
fast falling groups or two adjacent slow falling groups.
Furthermore, the separation of exit points at the top is exactly equal to
the separation of the group centers at the bottom (###), which would be
the opening points if these were two individuals falling straight down
with no tracking.
I will use the little (###) symbol to indicate an assumption or
simplification. In this case there are two. If they are not falling at
the same rate their freefall trajectories will be slightly different,
and if they are sliding around they can be a whole lot different.
----
We've barely started and already we see that relying just on mechanical
procedures is inadequate.
Any attempt at separation must include a social component.
If someone can't fall straight down they need to get some coaching.
Any attempt at separation must also include techniques beyond separation
of exit points, such as flying away from jumprun immediately after
opening.
However the main focus here is how to separate exit points.
----
Since separation of exit points equals separation of opening points
we can focus on the bottom end of the jump, the tracking and canopy
motion, and start estimating how much separation we want.
When we have that we can then focus on how to get that desired
separation when standing in the door on jumprun.
----
The bottom end of the jump looks like this:
UPPERS ------ > <------------------------------------- AIRPLANE
Group 2 Group 1
| |
| |
| < -- freefall -- > | The situation
| | at the moment
| | Group 2 opens
| |
/ \ / \
/ \ < -- track -- > / \
/ \ / \
surge surge surge surge
| | <----- ----->
| | | canopy canopy |
| | | motion motion |
| | | | | |
| | | | | |
|<--------O2------->| |<---------------O1-------------->|
opening pt opening pt
(Using the ground as the frame of reference) I've drawn the tracking
and canopy motion symmetrically as if there were no winds at opening
altitude, but any wind will affect both.
Now we can start estimating various distances. If you watch closely
during the handwaving parts you will see that at no time do my fingers
leave my hands.
----
Let's start with tracking.
How far apart should we be from our nearest neighbors, both within our
own group and from people from adjacent groups?
A typical canopy (###), say a Sabre loaded at 1.3, flies at about
30 mph = 44 ft/sec.
If we're facing someone head on we are closing at 60 mph = 88 ft/sec.
If we allow at least 3 seconds to see the other person, realize the
situation, and grab a riser to turn away, then (3 * 88 = 264 ) 300 ft
(###) looks like a good minimum to shoot for.
----
How far do people need to track to be at least 300 ft from people in
their own group for say a 4 way or an 8 way?
A A 300 ft
| \ open | B
212 ft | \ 300 ft \ 392 ft /
| \ \ | /
| \ \ | /
open---------X--------- B open---------X---------open
| / | \
| / | \
| / | \
| open | open
open open
4 way 8 way
If AB = 300 ft If AB = 300 ft
Then XA = 212 ft Then XA = 392 ft
150ft/sin22.5
x - x**3/3! +x**5/5!
sin22.5/57.3 = .38265
So 4 way - track 212 ft
8 way - track 392 ft
Now any winds at breakup and opening altitude will affect these
distances, but for the two people from adjacent groups tracking
towards each other about to become closest neighbors the effects
cancel (###). They may not track exactly the same amount of time
but the cancellation will be pretty close.
So that's the tracking estimate and we have:
UPPERS ------ > <------------------------------------- AIRPLANE
Group 2 Group 1
|<-------- Exit Separation --------->|
| |
| < -- freefall -- > | The situation
| | at the moment
| | Group 2 opens
| |
/ \ / \
/ \ < -- track -- > / \
/ \ / \
surge surge surge surge
| | <----- ----->
| | | canopy canopy |
| | | motion motion |
| | | | | |
| | | | | |
|<--------O2------->| |<---------------O1-------------->|
opening pt opening pt
| track2 | buffer | ??? | track1 |
|-------->|<------->|<------|<-------|
| 212 | 300 | ??? | 212 |
| 392 | | | 392 |
----
How much does a canopy surge on opening?
I don't know, so I'm going to ignore (###) it.
----
Also, a 300 ft buffer between adjacent groups is too small.
I know when I open and then find the following group in freefall it is
scary to see them too close. Neat, but scary.
And I know that if I'm tracking towards the previous group on breakup
I often have to half track or even angle off to keep from getting over
them.
I know from experience that I can not accurately judge my tracking
trajectory relative to fast moving canopies below me.
Hawks and falcons can do that, but I can't.
So let's take 500 ft (###) as a bigger buffer between adjacent groups.
----
Let's also allow a bit of sliding around. If groups are sliding at
random it will somewhat cancel itself out but a group could easily
slide 150 ft (###) from straight down in 60 seconds.
So let's let the two groups each slide 150 ft (###) towards the other.
Now we have:
| slide2 | track2 | buffer | CGS*T | track1 | slide1 |
|------->|-------->|<------->|<------|<-------|<-------|
| 150 ft | 212 ft | 500 ft | CGS*T | 212 ft | 150 ft |
| | 392 ft | | | 392 ft | |
|<--------------------- AGS * T ---------------------->|
| Exit Separation |
Where AGS = aircraft ground speed
CGS = canopy ground speed
T = seconds between between groups
AGS * T = slide2 + track2 + buffer + CGS * T + track1 + slide1
(AGS - CGS) * T = slide2 + track2 + buffer + track1 + slide1
slide2 + track2 + buffer + track1 + slide1 ft
T sec = -------------------------------------------- --------
(AGS - CGS) ft/sec
Now we can see why canopy motion becomes such a factor with strong
uppers. I guess this was obvious to anybody with good physical intuition
but I had to think about it for a while.
---------------------------------------------------------------------
Canopy ground speed, CGS, depends on the lower winds, the canopy air
speed, and which way it is facing.
Let's start with zero lower winds and canopies facing away from jumprun
after opening, so that CGS = 0, and see how much time we need for an
8 way following an 8 way, a 4 way following a 4 way, and a 1 way following
a 1 way.
This will give us a simplest case lower bound set of numbers for time
between exits.
150 + 392 + 500 + 392 + 150 1584 ft
8-8 T sec = ----------------------------- = ---------
--- AGS AGS
150 + 212 + 500 + 212 + 150 1224 ft
4-4 T sec = ----------------------------- = ---------
--- AGS AGS
150 + 0 + 500 + 0 + 150 800 ft
1-1 T sec = ----------------------------- = ---------
--- AGS AGS
With my mathematical hand waving gloves on I'm going to raise
that 800 ft solo followed by solo distance to 1000 ft (###),
because a lot of them will be post AFF people who really could
be sliding around, and they won't be hair triggered to dodge
on opening, and may not even know which way jumprun is.
I won't make it any higher because those solos tend to be in
the last half of the load and will tend to turn towards target
and away from the following person or group.
fudge factor 1000 ft
1-1 T sec = ----------------------------- = ---------
--- AGS AGS
6076 ft ft
1 knot = -------- = 1.688 ---
3600 sec sec
|-------|----------| |-------|-------|-------|
| AGS | AGS | | T | T | T |
| knots | ft/sec | | sec | sec | sec |
| | | | 8-8 | 4-4 | 1-1 |
|=======|==========| |=======|=======|=======|
| 100 | 168.8 | | 9.4 | 7.3 | 5.9 |
|-------|----------| |-------|-------|-------|
| 90 | 151.9 | | 10.4 | 8.1 | 6.6 |
|-------|----------| |-------|-------|-------|
| 80 | 135.0 | | 11.7 | 9.1 | 7.4 |
|-------|----------| |-------|-------|-------|
| 70 | 118.2 | | 13.4 | 10.4 | 8.5 |
|-------|----------| |-------|-------|-------|
| 60 | 101.3 | | 15.6 | 12.1 | 9.9 |
|-------|----------| |-------|-------|-------|
| 50 | 84.4 | | 18.8 | 14.5 | 11.8 |
|-------|----------| |-------|-------|-------|
| 40 | 67.5 | | 23.5 | 18.1 | 14.8 |
|-------|----------| |-------|-------|-------|
| 30 | 50.6 | | 31.3 | 24.2 | 19.8 |
|-------|----------| |-------|-------|-------|
| 20 | 33.8 | | 46.9 | 36.2 | 29.6 |
|-------|----------| |-------|-------|-------|
| 10 | 16.9 | | 93.7 | 72.4 | 59.2 |
|=======|==========| |=======|=======|=======|
|Exit Separation ft| |1584 ft|1224 ft|1000 ft|
| | | | | |
| slide + track + | | | | |
| buffer | | | | |
| | | | | |
| lower winds = 0 | | | | |
| CGS = 0 | | | | |
|-------|----------| |-------|-------|-------|
The top few rows look plausible but the bottom ones aren't so clear.
People in the early groups can't face 90 degrees away from the dropzone
for too long or they won't make it back, and who on top can count that
many seconds accurately? Indeed, who on top is even going to try?
So I'm thinking that just because we can do arithmetic doesn't mean
we have solved the problem, and maybe we should change the bottom few
rows like this to avoid misleading people into thinking there is some
scientific, four out of five leading doctors, official answer here:
|-------|----------| |-------|-------|-------|
| AGS | AGS | | T | T | T |
| knots | ft/sec | | sec | sec | sec |
| | | | 8-8 | 4-4 | 1-1 |
|=======|==========| |=======|=======|=======|
| 100 | 168.8 | | 9.4 | 7.3 | 5.9 |
|-------|----------| |-------|-------|-------|
| 90 | 151.9 | | 10.4 | 8.1 | 6.6 |
|-------|----------| |-------|-------|-------|
| 80 | 135.0 | | 11.7 | 9.1 | 7.4 |
|-------|----------| |-------|-------|-------|
| 70 | 118.2 | | 13.4 | 10.4 | 8.5 |
|-------|----------| |-------|-------|-------|
| 60 | 101.3 | | 15.6 | 12.1 | 9.9 |
|-------|----------| |-------|-------|-------|
| 50 | 84.4 | | 18.8 | 14.5 | 11.8 |
|-------|----------| |-------|-------|-------|
|-------|----------| |-------|-------|-------|
| 40 | 67.5 | | Not business as usual |
|-------|----------| |-------|-------|-------|
| 30 | 50.6 | | Look down |
|-------|----------| |-------|-------|-------|
| 20 | 33.8 | | Check for canopies |
|-------|----------| |-------|-------|-------|
| 10 | 16.9 | | Check the spot |
|=======|==========| |=======|=======|=======|
|Exit Separation ft| |1584 ft|1224 ft|1000 ft|
| | | | | |
| slide + track + | | | | |
| buffer | | | | |
| | | | | |
| lower winds = 0 | | | | |
| CGS = 0 | | | | |
|-------|----------| |-------|-------|-------|
---------------------------------------------------------------------
Now let's let people fly their canopies up jumprun towards the
following group and see what it takes to get separation.
slide2 + track2 + buffer + track1 + slide1 ft
T sec = -------------------------------------------- --------
AGS - CGS ft/sec
150 + 392 + 500 + 392 + 150 1584 ft
8-8 T sec = ----------------------------- = -----------
--- AGS - CGS AGS - CGS
150 + 212 + 500 + 212 + 150 1224 ft
4-4 T sec = ----------------------------- = -----------
--- AGS - CGS AGS - CGS
fudge factor 1000 ft
1-1 T sec = ----------------------------- = -----------
--- AGS - CGS AGS - CGS
We took a canopy air speed of 30 mph = 44 ft/sec so for zero lower winds
CGS = 44 ft/sec
( Let's note in passing that lower winds in the same direction
( as the uppers will give us better separation at opening and
( not worry about that case.
(
( Lower winds opposite the uppers aren't as common, although they
( happen here in Colorado pretty often, and they will give us
( worse separation.
(
( But, we don't have to do a whole separate table for them.
(
( We just notice that a 10 knot opposite wind on the bottom
( is equivalent to a 10 knot lower aircraft ground speed on
( top and so we can just look at the next row down for the
( answer. Unless we measured those lower winds on the way up
( with the GPS we're only guessing how strong they are anyway.
(
( This whole upper wind and separation business is filled with
( estimates and rules of thumb, but we only have to do it well
( enough to be safe and not cause too many go arounds.
|-------|----------|-----------| |-------|-------|-------|
| AGS | AGS | AGS - CGS | | T | T | T |
| knots | ft/sec | ft/sec | | sec | sec | sec |
| | | | | 8-8 | 4-4 | 1-1 |
|=======|==========|===========| |=======|=======|=======|
| 100 | 168.8 | 124.8 | | xx.x | xx.x | xx.x |
|-------|----------|-----------| |-------|-------|-------|
| 90 | 151.9 | 107.9 | | xx.x | xx.x | xx.x |
|-------|----------|-----------| |-------|-------|-------|
| 80 | 135.0 | 91.0 | | xx.x | xx.x | xx.x |
|-------|----------|-----------| |-------|-------|-------|
| 70 | 118.2 | 74.2 | | xx.x | xx.x | xx.x |
|-------|----------|-----------| |-------|-------|-------|
| 60 | 101.3 | 57.3 | | xx.x | xx.x | xx.x |
|-------|----------|-----------| |-------|-------|-------|
| 50 | 84.4 | 40.4 | | xx.x | xx.x | xx.x |
|-------|----------|-----------| |-------|-------|-------|
| 40 | 67.5 | 23.5 | | xx.x | xx.x | xx.x |
|-------|----------|-----------| |-------|-------|-------|
| 30 | 50.6 | 6.6 | | xx.x | xx.x | xx.x |
|-------|----------|-----------| |-------|-------|-------|
| 20 | 33.8 | -10.2 | | xx.x | xx.x | xx.x |
|-------|----------|-----------| |-------|-------|-------|
| 10 | 16.9 | -27.1 | | xx.x | xx.x | xx.x |
|=======|==========|===========| |=======|=======|=======|
| Exit Separation ft | |1584 ft|1224 ft|1000 ft|
| lower winds = 0 | | + | + | + |
| | | CGS*T | CGS*T | CGS*T |
|-------|----------|-----------| |-------|-------|-------|
Just doing that much of the table shows some limits on the validity
of this separation of exit points approach.
In the bottom two rows the canopies are moving across the ground
faster than the airplane is.
In the next couple rows up, aircraft ground speed of 30 or 40 knots,
it's going to take a really long time to separate exit points. The
first group could be at 1,000 ft or even on the ground and the initial
motivation, horizontal separation around opening altitude doesn't
even apply.
OK, let's fill in some of the seconds between groups rows and see
what happens.
|-------|----------|-----------| |-------|-------|-------|
| AGS | AGS | AGS - CGS | | T | T | T |
| knots | ft/sec | ft/sec | | sec | sec | sec |
| | | | | 8-8 | 4-4 | 1-1 |
|=======|==========|===========| |=======|=======|=======|
| 100 | 168.8 | 124.8 | | 12.7 | 9.8 | 8.0 |
|-------|----------|-----------| |-------|-------|-------|
| 90 | 151.9 | 107.9 | | 14.7 | 11.3 | 9.3 |
|-------|----------|-----------| |-------|-------|-------|
| 80 | 135.0 | 91.0 | | 17.4 | 13.5 | 11.0 |
|-------|----------|-----------| |-------|-------|-------|
| 70 | 118.2 | 74.2 | | 21.3 | 16.5 | 13.5 |
|-------|----------|-----------| |-------|-------|-------|
| 60 | 101.3 | 57.3 | | 27.6 | 21.4 | 17.5 |
|-------|----------|-----------| |-------|-------|-------|
| 50 | 84.4 | 40.4 | | 39.2 | 30.3 | 24.8 |
|-------|----------|-----------| |-------|-------|-------|
| 40 | 67.5 | 23.5 | | 67.4 | 52.1 | 42.6 |
|-------|----------|-----------| |-------|-------|-------|
| 30 | 50.6 | 6.6 | | 240.0 | 185.5 | 151.5 |
|-------|----------|-----------| |-------|-------|-------|
| 20 | 33.8 | -10.2 | | xx.x | xx.x | xx.x |
|-------|----------|-----------| |-------|-------|-------|
| 10 | 16.9 | -27.1 | | xx.x | xx.x | xx.x |
|=======|==========|===========| |=======|=======|=======|
| Exit Separation ft | |1584 ft|1224 ft|1000 ft|
| lower winds = 0 | | + | + | + |
| | | CGS*T | CGS*T | CGS*T |
|-------|----------|-----------| |-------|-------|-------|
My intuitive mental model of skydiving used to be that the airplane
and freefall were way up there in one world, and canopy flight was
down here in a totally separate and unrelated world.
In today's world of high altitudes, strong uppers and fast canopies
that is not true. I may be a couple miles below and behind but I'm
flying my canopy in the same world that airplane is.
To put it another way:
If I saw an airplane flying along dropping stuff, would I
fly over and get below and behind it?
That's what flying up jumprun right after opening amounts to.
Revised 2004-3-29 Skr
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