The first duct was made before I had obtained Marc Piolenc's book, so I really didn't have a clue. I just built a duct that looked about right and mounted it on the plane. But it didn't work. It was mounted too far forward, such that the inlet area was much too restricted. It perhaps could work, if it is remounted about 4 or 5 inches rearward of it's original location. This duct actually had lower static thrust than unducted, which told me right away something was wrong. Went back and reread Marc's book, and played around with some numbers, and came up with
Duct2. Here is a drawing showing the relative shape and location of Duct1, with Duct2 shown dotted in:
Here are some photographs, with Fan1 and Duct1 mounted on the plane. These photographs were taken in the fall of 1998.
The second duct was built in April, 1999. After experimenting with Fan2, then installing Duct1, had the same static thrust problems as before, so I knew there was a duct problem. Reviewed Marc's book, since I hadn't read it in awhile, then started playing with numbers. He says to maximize efficiency you need to maximize mass flow. So with this duct, I tried to maximize mass flow. However, I don't think that is the whole story, as there is a practical limit as to how far you can take it, and as exit area increases, I think the high-speed performance decreases. Also, the inlet and exit areas get larger as compared to the fan plane area, which results in a duct with more drag. With this duct, I increased the inlet area, taking into account the lost area due to the cross-sectional area of the engine cowl at the flight station of the duct inlet. This was the primary reason Duct1 didn't work. Also, in order to maximize mass flow, the inlet and exit areas are larger than the fan plane, resulting in a venturi effect, where the velocity of the air through the fan plane is 33% higher than the free-stream velocity.
Update 01-21-2000: I've finally figured out how to analyze the fan duct, taking into account drag, to determine max speed of the airplane. The results I achieved agree very well with reality, so that I can now design Duct3. See the
Duct3 page to see how my speed will improve.
RPM |
v0, knots |
v2, knots |
v4, knots |
v0, fps |
airframe drag |
duct drag |
thrust req. |
v2, fps in duct |
mass flow= |
v4, fps |
delta v |
thrust=mdot*deltav |
net thrust for accel. |
accel., f/sec2 |
accel. G |
3000 |
70.00 |
100.00 |
80.62 |
118.15 |
24.90 |
4.17 |
29.07 |
168.78 |
2.94 |
136.07 |
17.92 |
52.65 |
23.58 |
0.54 |
0.02 |
3500 |
80.00 |
110.00 |
88.68 |
135.02 |
32.52 |
5.45 |
37.96 |
185.66 |
3.23 |
149.67 |
14.65 |
47.34 |
9.37 |
0.22 |
0.01 |
4000 |
90.00 |
130.00 |
104.80 |
151.90 |
41.15 |
6.90 |
48.05 |
219.42 |
3.82 |
176.89 |
24.98 |
95.42 |
47.37 |
1.09 |
0.03 |
4500 |
100.00 |
150.00 |
120.93 |
168.78 |
62.66 |
8.51 |
71.17 |
253.17 |
4.41 |
204.10 |
35.32 |
155.64 |
84.47 |
1.94 |
0.06 |
5000 |
110.00 |
160.00 |
128.99 |
185.66 |
75.82 |
10.30 |
86.12 |
270.05 |
4.70 |
217.71 |
32.05 |
150.64 |
64.52 |
1.48 |
0.05 |
5500 |
130.00 |
180.00 |
145.11 |
219.42 |
105.90 |
14.39 |
120.28 |
303.81 |
5.29 |
244.92 |
25.50 |
134.87 |
14.58 |
0.34 |
0.01 |
6000 |
140.00 |
195.00 |
157.20 |
236.29 |
122.82 |
16.68 |
139.50 |
329.12 |
5.73 |
265.33 |
29.03 |
166.34 |
26.84 |
0.62 |
0.02 |
These numbers agree very well with my observations of 125 knots at 5200 RPM max. I normally cruise around 4500-4800 RPM and 100-110 knots, which is also in agreement.
Here is a cross-sectional drawing of Duct2:
And here are some photos of the plane with Duct2 and Fan3 installed:
Front Left View.
Another Front Left View.
Front Right View.
Another Front Right View.
Front View.
Front View, closeup of Duct2.
Rear View.
Rear Left View
Right Side View.
After flying Duct2 for several months, it was believed that the venturi- shape of Duct2 was possibly a mistake, that perhaps this shape was limiting the top-end speed of the aircraft. Duct3 was designed with a venturi of 10% (air velocity in the fan plane is 10% higher than aircraft velocity), a significant reduction from Duct2 that has 30%. Duct3 was designed in late 1999, then shelved for awhile. In January I discovered a method of predicting the max speed of the aircraft vs. fan RPM using outputs from the prop analysis program, then taking into account the venturi-effect of the duct and the drag of the airplane.
RPM |
v0, knots |
v2, knots |
v4, knots |
v0, fps |
airframe drag |
duct drag |
thrust req. |
v2, fps in duct |
mass flow= |
v4, fps |
delta v |
thrust= |
net thrust for accel. |
accel., f/sec2 |
accel. G |
3000 |
90.00 |
100.00 |
102.23 |
151.90 |
41.15 |
6.90 |
48.05 |
168.78 |
2.94 |
172.55 |
20.65 |
60.67 |
12.62 |
0.29 |
0.01 |
3500 |
100.00 |
110.00 |
112.46 |
168.78 |
50.81 |
8.51 |
59.32 |
185.66 |
3.23 |
189.81 |
21.03 |
67.95 |
8.63 |
0.20 |
0.01 |
4000 |
110.00 |
130.00 |
132.91 |
185.66 |
61.48 |
10.30 |
71.78 |
219.42 |
3.82 |
224.32 |
38.66 |
147.65 |
75.88 |
1.75 |
0.05 |
4500 |
130.00 |
150.00 |
153.35 |
219.42 |
105.90 |
14.39 |
120.28 |
253.17 |
4.41 |
258.83 |
39.41 |
173.69 |
53.41 |
1.23 |
0.04 |
5000 |
140.00 |
160.00 |
163.58 |
236.29 |
122.82 |
16.68 |
139.50 |
270.05 |
4.70 |
276.08 |
39.79 |
187.05 |
47.54 |
1.09 |
0.03 |
5500 |
160.00 |
180.00 |
184.02 |
270.05 |
160.41 |
21.79 |
182.21 |
303.81 |
5.29 |
310.59 |
40.55 |
214.42 |
32.21 |
0.74 |
0.02 |
6000 |
170.00 |
195.00 |
199.36 |
286.93 |
181.09 |
24.60 |
205.69 |
329.12 |
5.73 |
336.48 |
49.55 |
283.87 |
78.18 |
1.80 |
0.06 |
Here is a cross-sectional drawing of Duct3:
Duct2 is shown in dotted lines, for comparison.
It was originally thought that the max speed should increase from 125knots at 5200 RPM to about 150 knots. Initial flight testing has indicated that it might!
Results of the First Flight Test of Duct3
Duct3 was installed and flight tested for 1 hour at various altitudes up to 9500 feet on the morning of April 21, 2000. The duct is still in rough shape, with micro-balloon filler plastered all over it, so a drag reduction is possible just by completing the finishing process.
Duct3 performs only slightly better at cruise than Duct2, but it is significantly worse for static thrust and takeoff roll. There is a noticable lack of "punch" (acceleration) when starting the takeoff roll as compared to Duct2. It is estimated the takeoff distance was increased by maybe 10%. RPM throughout the flight range is reduced, from 5000 to 4800 at takeoff, from 5300 max to 5000 max at cruise. Top speed is around 130 knots at 5000 RPM, or about 10 knots shy of the predicted speed at that RPM. Thus, although it is true that for a given >RPM< Duct3 is faster, the increased venturi-shape of Duct2 allows the engine to run at a higher RPM, reducing the difference in speed between the two ducts.
A reader of this webpage faxed in a letter several months ago from EAA Experimenter magazine, about the ducted fan theory of the late Professor August Raspet of Mississippi State University. To read this very interesting letter, click
here.So now all doubts about the venturi-shaped Duct2 have been erased. Raspet was right. All aircraft using low speed (<200 mph) ducted fans should be using the Raspet duct, as Mr. Jenista says in his letter.
Duct3 was removed from the aircraft so that finishing work can be completed on it. Duct2 has been reinstalled so that flying can continue in the meantime. The stator blades were removed from Duct1, and this 7-bladed assembly will be modified such that it can be bolted into Duct2 or Duct3. Experiments will then continue to determine the effect of adding stators to these two ducts.
The 7-blade stator assembly was removed from Duct1 in June 2000, and installed in Duct2 such that it could be removed. Surprisingly, climb rate increased by almost 50% in some cases. No effect was noticed in takeoff distance or top speed.
Just recently (March 2001) I created a spreadsheet to try to determine why my performance never met up with predicted expectations from Marc de Piolenc's spreadsheet. His spreadsheet gives outputs of inlet and exit areas based on entering values for speed, RPM, HP, fan hub diameter, fan diameter, and other things.
I decided to try to understand what was going on by simplifying things as much as possible, and to reformat the spreadsheet to output thrust and power required, with the inlet, fan plane, and exit areas as inputs. Once this was done I could vary the inlet and exit areas and see what the effects were. This analysis makes several simplifying assumptions, and does not look at effects such as swirl or swirl HP. It mainly looks at just mass flow, the speeds v0, v2, v4, and the pressures p0, p2, p3, and p4. The major assumption made was that v2 = v3, the speed of air going through the fan cannot increase because of the duct, so the only thing the fan can do is increase pressure, p3. Total thrust has two components, Pressure Thrust, or (p4-p0)*A4, and Massflow Thrust, or (v4-v0)*mdot. This analysis may be completely incorrect, but I am posting it here to get some feedback from the experts. It does seem to predict reality, and shows some interesting effects related to exit area.
Here is the first analysis I performed, playing around with changing exit areas on Duct3:
A4 |
Power |
Pressure Thrust |
Massflow Thrust |
Total Thrust |
7.16 |
113 |
0 |
173 |
173 |
8.10 |
106 |
182 |
-9 |
173 |
8.50 |
100 |
247 |
-74 |
173 |
9.00 |
90 |
321 |
-147 |
173 |
Here we see some interesting things happening. With Duct3 as designed, with an exit area of 7.16 square feet, all the thrust is from massflow, none is from pressure. 113 HP is required to produce a thrust of 173 pounds to go 160 knots.
Now, there is quite a jump from 7.16 to 8.10, some intermediate values would show Pressure Thrust increasing while Massflow Thrust decreases. But here, with the change from 7.16 to 8.10, all the thrust reverts from Massflow Thrust to Pressure Thrust. Once Massflow Thrust goes to zero, exit velocity v4 is equal to ambient velocity v0, and all thrust is due to pressure created by the fan HP.
It is probably not desirable to have exit velocity less than ambient velocity, but it is interesting that as you continue to increase exit area, the ability of the HP to produce thrust becomes more efficient. You can see that less HP is required to produce the same 173 pounds of thrust.
Because of this possibility of increased thrust with less HP, I've decided to modify Duct3, to increase it's exit area. This actually makes the cross-section look better. Duct3 was supposed to be a high-speed duct, but it didn't turn out that way, because it lugged the engine down. I'm hoping that increasing the exit area will allow the RPM to come up again, and increase my speed to about 140 knots.
Here are some interesting results from an analysis of Duct2, the duct I've had the most success with to date, and for which I've done most of my 150 hours of flying. With A0=9.76, an A0/A2 ratio of 1.33, A2=7.32, and A4=9.02, an A4/A2 ratio of 1.23, we get the following results:
v0 |
Power required |
Fuel Burn |
Pressure Thrust |
Massflow Thrust |
Total Thrust |
mdot |
Fan RPM |
mpg |
80 |
14 |
1.2 |
9 |
35 |
43 |
3.13 |
3403 |
77 |
100 |
27 |
2.4 |
14 |
54 |
68 |
3.92 |
4253 |
48 |
100 |
0 |
0.0 |
-52 |
54 |
2 |
3.92 |
||
120 |
64 |
5.7 |
23 |
96 |
119 |
4.70 |
5104 |
24 |
This shows that Duct2 is using a combination of Pressure Thrust and Massflow Thrust. But the results for Duct3, with A0=8.05, an A0/A2 ratio of 1.10, A2=7.32, and A4=7.16, an A4/A2 ratio of 0.98, shows it's thrust is all Massflow:
v0 |
Power required |
Fuel Burn |
Pressure Thrust |
Massflow Thrust |
Total Thrust |
mdot |
Fan RPM |
mpg |
100 |
28 |
2.5 |
0 |
68 |
68 |
3.23 |
3518 |
46 |
120 |
48 |
4.3 |
0 |
98 |
98 |
3.88 |
4221 |
32 |
160 |
113 |
10.1 |
0 |
174 |
174 |
5.17 |
5628 |
18 |
So my next experiment, currently under construction, is to modify Duct3 to increase it's exit area. Increasing the exit area to 8.5 square feet, an A4/A2 ratio of 1.16, slightly greater than the A0/A2 ratio of 1.10, gives the following results:
v0 |
Power required |
Fuel Burn |
Pressure Thrust |
Massflow Thrust |
Total Thrust |
mdot |
Fan RPM |
mpg |
80 |
12 |
1.1 |
62 |
-18 |
43 |
2.59 |
2814 |
84 |
100 |
24 |
2.2 |
97 |
-29 |
68 |
3.22 |
3518 |
52 |
120 |
42 |
3.8 |
140 |
-42 |
98 |
3.86 |
4221 |
36 |
140 |
67 |
5.9 |
189 |
-57 |
132 |
4.51 |
4925 |
27 |
160 |
100 |
8.9 |
247 |
-74 |
173 |
5.17 |
5628 |
21 |
180 |
142 |
12.7 |
313 |
-94 |
220 |
5.81 |
6332 |
16 |
180 |
0 |
0.0 |
96 |
-94 |
3 |
5.81 |
6332 |
|
200 |
195 |
17.4 |
387 |
-115 |
272 |
6.27 |
7036 |
13 |
If these numbers are real, then achieving a 140 knot cruise speed with a 6 gallon per hour burn rate and 27 mpg efficiency, would be a little closer to normal Long-EZ performance. Actually I would be happy to achieve 140 knot cruise with only 20 mpg efficiency. Currently, with Duct2, I'm only doing about 110 knots at 6.5 gph and 20 mpg efficiency.
We can see from this picture, that the modified Duct3 has better lines than the original, less external tail cone, hopefully less chance for the airflow to separate and add drag. When this is built and tested, the results will be posted here.
Update, 3-4-02, I'm just flying these days, not doing much experimenting, but here is my latest thinking for the future: A smaller diameter, higher RPM ducted fan, will probably have 5 blades, especially if turbocharged.