**Design of E-Props Propellers for aircraft**

**LmPTR©** **software** - some theory

The E-PROPS design department consists of **5 technicians and engineers** (it means 25% of the staff). The head of this department is Jérémie Buiatti. They realize the theoretical calculations, the modelling, the development of prototypes and all experiments in the bench test system and during flights.

The design department establishs the specifications of each propeller by taking into account:

- The characteristics of the engine (power, troque, thrust, RPM)
- The airframe which is going to be equipped with this optimized engine + propeller

(puller or pusher configuration, aerodynamic characteristics, wings / fuselage interaction...)

- The required performances of the aircraft
- The conditions of use and the missions of the aircraft

The team uses successful CAD softwares, and have developed an iterative inhouse program : **LmPTR©**.

**AIRCRAFT PROPELLERS OPTIMIZATION PROCESS**

To optimize a propeller, for a specific engine and a specific aircraft, is a complex task because :

- flight speed, engine RPM and power are compulsory

- propeller diameter is limited either by aircraft geometry (ground clearance or fuselage clearance) or by peripheral speed (supersonic issues).

Propulsion efficiency factor is calculated from propeller diameter and engine power. This efficiency factor is the max achievable propeller efficiency. Then, it is up to the propeller designer to come closer to this limit.

The available optimization parameters are :

- number of blades

- blade loading distribution vs span

- chord distribution

- pitch distribution

- airfoil vs span

To increase number of blades allows reducing lift of each blade. So the induced drag of each blade is reduced. But, with a constant chord, this increases the friction drag. And if chord is reduced, Reynolds number decreases and airfoils characteristics are degraded. Use of small chords also leads to mechanical strength issues.

When looking for the optimum load distribution, Induced drag must be taken into account. For example, blade tip cannot generate high lift without high induced drag.

Chord optimization leads to use each airfoil at best lift/drag ratio, without forgetting Reynolds variation effects and checking airfoil matching to CL conditions (Reynolds and Mach).

Pitch distribution is used to maintain an optimum lift coefficient to each airfoil in order to get the chosen lift distribution with the optimized chord and airfoil distribution.

**Linked to this complex process, propeller design is an iterative calculation. The modification of one parameter leads to change the others.**

**IN HOUSE SOFTWARE ***LmPTR©*

*LmPTR©*

*LmPTR©* has been developed by Helices E-Props engineers, especially by Jérémie Buiatti.

Numerical processing and sharpness software modeling allow an efficient design process, able to get the optimum propeller for each flight configuration.

This software performs a detailed aerodynamic flows analysis and a mechanical behavior analysis of the propeller.

This software is implemented from an advanced language and contains more than **57000 code lines**. The software implementation was carried out along 3 years of work. ** LmPTR©**sofware is regularly improved thanks to ground and flight tests data on wood then on carbon E-Props propellers.

Tests have also been made in a **wind tunnel**, during carbon propellers' developments for UAV. These tests are at the moment confidential and cannot be published. They have allowed to verify numerous hypotheses and to enrich the **LmPTR©** software.

This sofware is an asset for a propeller manufacturer. It allows to quickly design propellers right adapted to specific aircraft and engine.

Propeller geometrical data are then sent to the numerical control machining center which manufactures the propeller (wood one) or the mold (composite one)

This software allows the team to imagine new propellers concepts, by using particular geometries and profiles developed inhouse. That is why E-PROPS propellers are very different from other propellers proposed at present on the market.

On certain models, **7 innovations** can be found compared with the traditional propellers. Some of those innovations have been patented. Hélices E-PROPS are propellers of 3rd generation. The obtained performances are exceptional.

* ***LmPTR©** software on the 2018-01-16 :

**LmPTR©**

- 9500 hours of design

- 57000 code lines

- data of 284 prototypes tested

- enhanced by the data of 47 tests campaigns on ground and on flight

An exceptional tool to design the propellers of third generation

_________________________________________________________________________________

**PROPULSION THEORY : JUST A LITTLE ! **

In order to understand the propeller operation, it is simpler to perform the analysis at propeller level rather than at airfoil level.

First, the third Newton law assess : "If a part A applies a force FA on a part B, The part B applies a force FB on the part A. FB has the same value than FA, the same line of action but the opposite direction". This law is summarized by "action=reaction" principle.

If we want our propeller A use a forward force, it must apply on "B" a backward force. For the aircraft, "B" is the air mass going though the blades swept disc. It is not really a mass but a mass air flow. This "mass air flow" is equal to "disc surface" x "air speed" x " air density".

To apply a force on the mass air flow, blades are like wings. Blade airfoils allow propeller to apply lift forces on air flow. The propeller applies a force on the air flow so the air flow speed is modified.

The difference between the upstream air speed and the downstream air speed is calculated as followed :

Delta Velocity (upstream/downstream) = pull / mass air flow DV = P / dm

*from the second Newton law : F = d(m.v)/dt *

This speed variation induced by the pull is applied half upstream and half downstream.

Mass air flow is so equal to : Dm = mvo x Sdisc x (Vflight + DV/2)

with :

- mvo : air density (kg/m^3)

- S disc : blades swept disc (m²)

- Vflight : Flight speed

Some power calculations can be carried out :

- usefull power delivered by the propeller to the aircraft : Pu = Pull x Vflight

- absorbed power : Pa = Pull x (Vflight + DV/2)

So propulsion efficiency factor : **rp = Pu / Pa **

==> propulsion efficiency factor is an absolute limit which is the design goal for the propeller designer.

Choice of a small diameter for the propeller leads to mediocre performances. And this becomes worst with a low flight speed.

Number of blades may allow reducing the performance loss (see after in the text). But this cannot be enough to reach the performances with an adapted diameter.

Propulsion phenomenon power losses cannot be decreased by the propeller designer. But he must take care not to increase them with a bad pull distribution along the propeller disc. So he must chose the right pitch, chord and airfoil distribution in order to get the optimum lift distribution. Unfortunately, others energetic losses exist : losses linked to blade drag. Blades are like wings and generate lift and drag. This drag consists of 2 parts : friction drag and lift induced drag

**1/ Friction drag on blade airfoils **

Drag = 0.5 x Mvo x S x CD x V²

Blade case is more complex than wing one, because speed is variable from foot to tip of the blade.

*At blade foot :*

Low speed and small chord lead to ridiculous Reynolds number => airfoil performances are mediocre (high CD and low CLmax)

*At blade tip : *

High speed and very small chord => Reynolds number remains small.

But as the speed is close to sound one, Mach number is high. High Mach leads to airfoil characteristics degradation. With a small curvature or incidence defect, airflow may become supersonic and so generate noise and degrade performances.

**2/ Lift induced drag **

The wing has a finite span and so lift generate induced drag. Air speed is constant along the span. Induced drag can be calculated easily at wing level.

For the propeller blade, induced drag modeling is not easy because of the variable speed along the span. For this drag assessment, Helices E-Props engineers don't find adapted calculation method in specialized press or in labs studies reports. So the team has implemented a new and efficient calculation method. calculation duration is quite long : 90% of the airflow modeling duration is used to define induced effects on blades linked to iterative documentation.

This chapter has listed causes of propeller propulsion energetic losses. Trigonometric aspects of the modeling have not been presented because they are out of scope of this simplified explanation of the modeling process.

*Jérémie Buiatti*

*Research Manager - Hélices E-Props [2010]*