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Email from Bill during one of the legendary
winds and spotting discussions on rec.skydiving
(with a few tweaks to the arrows in the ascii drawings so they don't
get interpreted as HTML comments).
From Bill Von Novak Tue May 16 11:26:11 1995
Subject: some examples
skratch -
i went through the math on some examples. i figured you might be
able to use them.
***********************************************************************
A few spotting examples (with just a little math.) I am just
considering distance from group 1's canopies to group 2 as they open -
I'm not considering if the spot is a practical one or if the winds are
safe to land in. I'm also assuming that 500 feet is the minimum safe
separation at opening time.
CASE 1: no wind, 1000 feet separation (skratch rules)
Exit spacing = (airplane speed - wind speed) * time, so ~6 seconds
gives you 1000 feet. Jumpers follow the same trajectory. Separation is
decreased by tracking (assumed to be 100 feet per jumper) and canopy flight
in the first group (assumed to be 25 mph * 6 seconds, or 220 feet.) We have
to assume a worst-case of canopy flight out from the center, since that's
what the jumper should be doing for the first few seconds. We look at the
point in time when the second group has broken off and is about to pull.
We started with 1000 feet, minus 220 feet for canopy flight of the
first group, and 100 (x2) feet for tracking. We're left with 580 feet.
Looks good. Diagram below:
note: group spreads out as jumpers track off, then deploy.
also note: vertical scale at bottom end is greatly exaggerated - the two
groups would actually be at almost the same altitude.
AIRCRAFT SPEED:120 MPH
MAX TRACK:100 FEET
CANOPY SPEED:25 MPH
group 1 group 2 |\
-----------------------------------------------[=0==>----------- > JUMP RUN
* -- 1000 FEET -- * | 12000
* (6 SECONDS) * |
* * | NO WIND
* * |
* * |
* * |
* * |6000
* * |
* * |
* * | NO WIND
* * |
* * |
* * |BREAKOFF ALT
where group * * * * |3000
1 will be * * 222 --opening alt, group 2 |
when group 2 * * |OPENING ALT
opens -- > 111111111 |
|
MIN HORIZ SEP |
|--580 FEET--| |
------------------------------------------------------------------
=========================================================================
CASE 2: 30 mph wind, 1000 feet separation
Again, Exit spacing = (airplane speed - wind speed) * time, so ~7.5 secs
gives you 1000 feet. Jumpers all follow the same trajectory. Separation is
decreased by tracking (assumed to be 100 feet per jumper) and canopy flight
(assumed to be 25 mph * 7.5 seconds, or 275 feet.) However, winds blow the
first group away from the second group, so we add (30 mph * 7.5 sec) or 330
feet.
We started with 1000 feet. Subtract 275 feet for canopy flight of the
first group, add 330 feet for wind induced separation, and subtract 200 feet
for tracking again. We're left with 850 feet. Looks even better now.
AIRCRAFT SPEED:120 MPH
MAX TRACK:100 FEET
CANOPY SPEED:25 MPH
-------------------------------------------------------------- > JUMP RUN
* -- 1000 FEET -- * | 12000
* (7.5 SECONDS) * |
* * |
* * |
* * |
* * |
* * |6000
* * |
* * | WIND
* * | < --30 MPH
* * |
* * |BREAKOFF ALT
* * * * |3000
* * 222 |
* * |OPENING ALT
11111111 |
|
MIN HORIZ SEP |
| -- 850 FEET -- | |
-----------------------------------------------------------------
===========================================================================
CASE 3: 30 mph wind at altitude, 0 mph at opening, 1000 feet separation
Again, Exit spacing = (airplane speed - wind speed) * time, so ~7.5 secs
gives you 1000 feet. Jumpers all follow the same trajectory. Separation is
decreased by tracking (assumed to be 100 feet per jumper) and canopy flight
(assumed to be 25 mph * 7.5 seconds, or 275 feet.) There is no wind at
opening, so the group is not moved in any direction
We started with 1000 feet, subtract 275 feet for canopy flight of the
first group and 200 feet for tracking again. We're left with 525 feet.
Uh oh. Getting closer.
Why is this jump different from the first one? The groups are waiting
longer between exits, so the canopies have more time to wander away from
the center of the group. (and no, we can't assume they're going to do
any differently. They SHOULD be moving away from the center for the
first few seconds, which is the worst case.)
AIRCRAFT SPEED:120 MPH
MAX TRACK:100 FEET
CANOPY SPEED:25 MPH
-------------------------------------------------------------- > JUMP RUN
* -- 1000 FEET -- * | 12000
* (7.5 SECONDS)* | WIND
* * | < --30 MPH
* * |
* * |
* * |
* * |6000
* * |
* * |
* * | WIND 0 MPH
* * |
* * |BREAKOFF ALT
* * * * |3000
* * 222 |
* * |OPENING ALT
111111111 |
|
MIN HORIZ SEP |
|--525 FEET--| |
-----------------------------------------------------------------
===========================================================================
CASE 4: 30 mph wind at altitude, -15 mph at opening, 1000 feet separation
(i.e. wind at opening altitude is 180 degrees different.)
Exit spacing = (airplane speed - wind speed) * time, so ~7.5 secs
gives you 1000 feet. Jumpers all follow the same trajectory. Separation is
decreased by tracking (assumed to be 100 feet per jumper) and canopy flight
(assumed to be 25 mph * 7.5 seconds, or 275 feet.) Separation is also
decreased by winds blowing the first group back towards the second one.
Since the second group hasn't traversed this space yet, the winds have
not yet blown them anywhere. so we have to subtract an additional
(15 mph * 7.5 seconds, or 165 feet.)
We started with 1000 feet, subtract 275 feet for canopy flight of the
first group, 165 feet for wind drift, and 200 feet for tracking again.
We're left with 360 feet. Too close.
AIRCRAFT SPEED:120 MPH
MAX TRACK:100 FEET
CANOPY SPEED:25 MPH
-------------------------------------------------------------- > JUMP RUN
* -- 1000 FEET -- * | 12000
* (7.5 SEC) * |
* * |WIND
* * | < --30 MPH
* * |
* * |
* * |WIND
* * | --- 0 MPH
* * |
* * |6000
* * |WIND
* * | - > 15 MPH
* * |
* * |BREAKOFF ALT
* * * * |3000
* * 222 |
* * |OPENING ALT
111111111 |
|
MIN HORIZ SEP |
|-360F-| |
-----------------------------------------------------------------
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