# Schübeler WIKI: The power to weight ratio

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Case Study: Minijets Stinger with DS-51-AXI HDS and HET 700-68-1125kV

In order to avoid a disappointment due to unexpected flight behaviour or insufficient performance of the planned model, we would like to take the opportunity to present some substantiated criteria enabling the realisation of the favoured characteristics for the model.
A simple calculator is sufficient for all the indicated formulas. The required data are easily definable with the manufacturer information or by means of a scale (weight).

An important point when choosing the right fan unit for the model is the power/weight ratio. In contrast to the thrust/weight ratio this also considers exhaust speed (all calculations refer to max. battery voltage).

Power/weight ratio:

$$P_{spezges} = {P_{abges} \over m_{ges}}$$

$$P_{abges}$$ refers to the output power, $$m_{ges}$$ refers to the overall model weight. This is determinable with a scale or can be calculated after having chosen the fan system. $$P_{ab}$$ can be calculated with thrust and exhaust speed data which are available in our measurement diagrammes.

In order to get $$P_{abges}$$ it is also important to consider the efficiency factor of the channels of our model.

$$P_{ab}$$ from exhaust speed and thrust:

$$P_{ab} = {S \cdot c \over 2}$$

e.g..: S=55 N, c=94 m/s: (51HDS with HET 700-68-1125kV)

$$P_{ab} = {55N \cdot 94m/s \over 2} =2585W$$

The efficiency factor of the channels $$\eta _{kanal}$$ at the extreme could reach values of about 65%. Such an extreme case could occur for example with high velocity models at standstill.

With these fast models and an advantageous design of the ducted fan the efficiency factor will increase remarkably during the flight due to more beneficial inlet flow and a more effective flow around the blades.
Consequently, the efficiency factor of the channel adopts different values depending on the model and flight phase.

In the following you can find estimated factors which occur during the flight:

• Short Airliner nacelle, large intake lip radius (e.g. models like Airbus A-300, Boeing 737)

$${\eta _{kanal} \approx 0,95}$$

• Long straight nacelle (e.g. ME-262)

$${\eta _{kanal} \approx 0,9}$$

• Very long, but straight channels (e.g. MiG-15 etc. but also SU-27)

$${\eta _{kanal} \approx 0,85}$$

• Curved channels with small cross-sections, small intake lip radius (e.g. Vampire, F-16, Pampa etc.)

$${\eta _{kanal} < 0,85}$$

These values are considered as approximate indications for informational purposes about the different flow conditions according to the model.
In order to incorporate $$\eta _{kanal}$$ it is necessary to simply multiply $$P_{ab}$$ with the corresponding value for $$\eta _{kanal}$$.

e.g.: $$\eta _{kanal} = 0,85$$

$$P_{abges}=\eta _{kanal} \cdot P_{ab} = 0,85 \cdot 2585W =2197W$$

The resulting value (P abges) now has to be plugged into the first equation and then divided by the model weight (e.g. Minijets Stinger 3,7kg).
That way we receive a parameter for our model which enables us to estimate its flight performance with assistance of the following table.

$$P_{spezges} = {2197W \over 3,7kg} =594W/kg$$

Model type: $$P_{spezges}$$

• high speed model: 500 – 800 W/kg
• sporty Jet, Trainer: 300 – 500 W/kg
• moderate speed Jet (Me-262, A-10 etc.): 200 – 300 W/kg
• Airliner, Transporter: 150 – 200 W/kg

The values indicated in the table above refer to battery peak voltage; they are on the high-performance side and are well-achievable with our propulsion systems.

Thus, for example an Airliner can still be flown securely with considerably less power.

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