Re: [indoor construction] VP or VD

From: markdrela <drela_at_mit.edu>
Date: Tue, 24 Oct 2006 01:24:20 -0000

--- In Indoor_Construction_at_yahoogroups.com, "Slobodan Midic"
<slomi_at_...> wrote:
>
> 1. There are two ways for reducing prop RPM
> in "low ceiling" space in the beginning of flight:
> VP and VD. From the point of prop efficiency
> what method has more advantages than others,
> and why?

Theoretically, the VD prop is better, by far.
The VD prop reduces climb mainly by releasing the rubber's energy more
slowly during the power burst, via a greatly reduced rpm. The VP prop
reduces climb mainly by throwing away most of the rubber's energy
during the power burst, via blade stall.

Out of curiosity, I just briefly looked at the VD design problem.
Here's are some first impressions:

1) The baseline minimum-diameter design wants to have a smaller
diameter than usual, with signficantly wider blades. For F1D, a 20 cm
radius with 9 cm max blade chord looks pretty good.

2) The pitch wants to be progressively smaller towards the center, by
about 2-3 degrees, so that the design blade cl's might increase from
0.3 at the root to 0.5 at the tip. This will mitigate the "bad" twist
which results from the blade being moved outward at high torque. (A VP
prop wants to have a roughly uniform baseline pitch).

3) The smaller baseline diameter allows one to use a larger max/min
diameter range for a given wing. For F1D, increasing the radius from
the 20 cm to 27 cm looks pretty good. It's essential that the blade
angles also increase about 7 degrees at the same time, so that the
blade cl's are still good. The innermost 1/3'rd of the blade will now
be stalled, but the outer 2/3'rds will be close to max cl/cd, so that
the efficiency is still pretty good. (In contrast, a VP prop must be
fully stalled at high pitch, with terrible efficiency).

I calculate the following for the min-D, mid-D, and max-D points, to
match level-flight thrust requirement:

R = 20 cm
delta pitch = 0 deg
V = 0.67 m/s
Thrust = 0.0036 N = 0.367 gf
Torque = 0.000579 N-m = 5.9 gf-cm = 0.082 in-oz
RPM = 56.0
efficiency = 71.0%

R = 23 cm
delta pitch = 3 deg
V = 0.67 m/s
Thrust = 0.0036 N = 0.367 gf
Torque = 0.000798 N-m = 7.9 gf-cm = 0.113 in-oz
RPM = 40.9
efficiency = 70.6%

R = 27 cm
delta pitch = 7 deg
V = 0.67 m/s
Thrust = 0.0036 N = 0.367 gf
Torque = 0.001187 N-m = 12.1 gf-cm = 0.168 in-oz
RPM = 29.1
efficiency = 66.6%

Note the small torque at cruise at min-D, and the very large allowed
torque increase (roughly twice!) at max-D without climbing. So this
prop will want a long motor, wound to nearly max turns even in lowish
ceilings. The initial climb rate at 0.5 in-oz will be similar to that
 of a fixed-pitch prop at 0.25 in-oz, and with a vastly lower climb
RPM to boot.

The duration potential is best deduced via an energy argument:
Since you're taking off with nearly max energy, and not dumping it via
blade stall like with VP, theoretically you should be able to get
high-ceiling durations with only a fraction of the total climb altitude.
Received on Mon Oct 23 2006 - 18:26:05 CEST