5.0004809

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Propulsion selection method using motor thrust table for optimum flight in
multirotor aircraft
Conference Paper in AIP Conference Proceedings · April 2020
DOI: 10.1063/5.0004809
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Propulsion selection method using motor
thrust table for optimum flight in multirotor
aircraft
Cite as: AIP Conference Proceedings 2226, 060008 (2020); https://doi.org/10.1063/5.0004809
Published Online: 22 April 2020
H. M. Putra, M. R. Fikri, D. P. Riananda, G. Nugraha, M. L. Baidhowi, and R. A. Syah
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AIP Conference Proceedings 2226, 060010 (2020); https://doi.org/10.1063/5.0006800
AIP Conference Proceedings 2226, 060008 (2020); https://doi.org/10.1063/5.0004809
© 2020 Author(s).
2226, 060008
Propulsion Selection Method Using Motor Thrust Table for
Optimum Flight in Multirotor Aircraft
H. M. Putra1, a), M. R. Fikri2, b), D. P. Riananda1, c), G. Nugraha1, d), M. L.
Baidhowi1, e), and R. A. Syah3, f)
1
2
Drone Research Squad, IoT Research Department, PT. Bukalapak.com, DKI Jakarta, Indonesia.
Head of IoT & Physics Lab, Information System, Sampoerna University, DKI Jakarta, Indonesia
3
Head of IoT Research Department, PT. Bukalapak.com, DKI Jakarta, Indonesia.
a)
Corresponding author: [email protected]
b)
[email protected]
c)
[email protected], [email protected]
d)
[email protected]
e)
[email protected]
f)
[email protected]
Abstract. One of the problems when designing an aircraft is flight time estimation. When we design the aircraft, in general,
calculating the maximum takeoff weight becomes the priority. The longer flight time required by the aircraft, the more
batteries should be added. More batteries mean the payload capacity of the aircraft is decreased. On the other hand, adding
more weight will increase the requirement of using more powerful motors. We need to take into our account, that using
powerful motors should be calculated carefully because the current consumption is also increased. This problem is circling
in the same situation, without any real solution to overcome the problem. As unmanned aircraft has become a critical part
of human life for example in surveillance, agricultural, and medicine delivery mission, obtaining the optimum and efficient
flight time is vital. In this research, we propose a novel approach of maximum takeoff weight calculation that is needed
when designing the aircraft by looking at the complete map of motor specifications. The goal of this paper is to help any
aircraft user from hobbyist to professional to determine whether their aircraft design is feasible.
INTRODUCTION
Nowadays, Unmanned Aerial Vehicles (UAVs) are common technology in the world. There are two main
categories based on its component where a lift is produced which is fixed-wing and rotary-wing.1 The fixed-wing
aircraft produces its lift by non-movable wing attached to its body. Meanwhile, the rotary-wing produces its lift from
moving wing in a circular motion known as a propeller. The rotary-wing has many advantages such as vertical takeoff and landing, low speed and stationary flight, and no need for runway.2
There are subcategories for rotary-wing based on its number of rotors: single-rotor and multirotor UAV. Multirotor
UAV has many rotors, for example, four, six, and eight. Multirotor UAV uses its thrust to lift and to control its attitude.
However, multirotor has one disadvantage, it requires high power consumption.
When designing the multirotor, generally start from defining maximum take-off weight (MTOW) and payload. If
we are not considering the weight of the propulsion system and batteries earlier, there will be a later problem. One of
the examples is when the actual flight time does not meet the specification, adding one or more batteries to make it
fly longer is not a solution. The additional battery will add overall weight and reducing payload capacity. Meanwhile,
changing motor with a new powerful motor will increase current consumption and obviously, larger battery capacity
is needed. This process of selecting the payload and battery will occur repeatedly and become the problem that should
have a solution since it is time-consuming and costly.
7th International Seminar on Aerospace Science and Technology – ISAST 2019
AIP Conf. Proc. 2226, 060008-1–060008-7; https://doi.org/10.1063/5.0004809
Published by AIP Publishing. 978-0-7354-1985-8/$30.00
060008-1
In order to tackle this repeated problem, in this study, we propose a method to measure and estimate the capability
of the motors then produce information about the recommendation of payload capacity on the Thrust Table. We
elucidate the detail information start from calculating the motor thrust data in section 2, the steps of creating the Thrust
Table in section 3, then the discussion of the Thrust table in section 4 with the conclusion and future work in section
5.
MOTOR THRUST DATA
In this method, first, we collect every motor thrust and current consumption data. We are using thrust and current
consumption with specific motor types and propeller combination from T-Motor as our research data. Those data also
can be acquired by using a thrust benchmark system.3
FIGURE 1. Example curve. Thrust and current relation of T-Motor MN501s kv3601
Thrust and Current Relation
The thrust data and current consumption can be fit into a curve. For every different combination, e.g. the same
motor but for different propeller or vice versa, need a new curve. From that curve, we can make an approximation
using second-order polynomial. The general form of the polynomial equation can be expressed4 as Eq. (1).
𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
(1)
Where
𝑓(𝑥) is the value of Y-axis, the output of the polynomial function
𝑎, 𝑏, 𝑐 are constants for second order polynomial
𝑥
is value of X-axis
In this case, 𝑓(𝑥) is current in Ampere and 𝑥 is thrust in kg. Because the curve intersects with point (0,0) so there
will be no c. So, we can write the relation between thrust and current as Eq. 2. This approach makes a possibility to
estimate motor thrust and current relation without knowing the actual motor scientific model.
𝐼 = 𝑎𝑥 2 + 𝑏𝑥; 0 ≤ 𝑥 ≤ 𝑥𝑚𝑎𝑥
Where
𝐼
is current consumption in Ampere (A)
𝑎, 𝑏 are constants from second order regression
𝑥
is thrust in kilogram (kg)
𝑥𝑚𝑎𝑥 is maximum thrust (kg)
1
Data source: http://store-en.tmotor.com/goods.php?id=697 (17 July 2019)
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(2)
Where 𝑎 and 𝑏 are constants, 𝑥 is the amount thrust needed, and 𝐼 is current consumption. There is a limit for
thrust, it is a maximum value from specification data. We should make a limit in later formula.
Calculating Required Battery
From the known current usage and flight time required, we can use Eq. (3) to estimate the required battery capacity.
The 1 Ampere-hour means that the battery will supply 1 Ampere for an hour.5 Multiplying total current consumption
and time will result in battery capacity and total current consumption can be acquired by multiplying current usage
per motor with the number of motors.
𝑡
𝐶𝑟𝑒𝑞 = 1.25 ∙ 𝑛 ∙ 𝐼 ∙ 𝑚𝑖𝑛
(3)
60
Where
𝐶𝑟𝑒𝑞 is battery capacity in Ampere-hour (Ah)
𝑛
is number of motors in multirotor
𝐼
is current usage per motor in Ampere (A)
𝑡𝑚𝑖𝑛 is flight time required in minute
The current I from the Eq. (2), can be inserted into Eq. (3) in Ref. 6. The result is the required battery capacity in
Ampere-hour (Ah). The unusable and spare battery capacity also needs to be considered. When the capacity below
10%, the battery should stop discharging.7 For safety reason and possible emergency case, 20% of total battery
capacity should be reserved. So, extra value 125% of battery capacity needs to be expected. One thing to note, this
calculation does not include the battery discharge characteristic.8 Most batteries have less capacity when discharged
with a higher current. Lithium batteries are well known to have a quite linear characteristic between capacity and
discharge rate. So, this method uses an assumption of the linearity of lithium battery.
After we get the required battery capacity, we need to calculate the number of parallel cells. There is an input value
of real battery capacity. Simply using Eq. (4).
𝑛𝑝𝑎𝑟 = 𝑐𝑒𝑖𝑙𝑙𝑖𝑛𝑔 (
𝐶𝑟𝑒𝑞
𝐶𝑟𝑒𝑎𝑙
)
(4)
Where
𝑛𝑝𝑎𝑟 is number of parallel cells
𝐶𝑟𝑒𝑞 is required battery capacity (Ah)
𝐶𝑟𝑒𝑎𝑙 is real battery capacity (Ah)
The total battery cells required can be calculated in Eq. (5) using result from Eq. (4).
𝑛𝑡𝑜𝑡 = 𝑛𝑝𝑎𝑟 ∙ 𝑛𝑠𝑒𝑟
(5)
Where
𝑛𝑡𝑜𝑡 is total number of cells
𝑛𝑝𝑎𝑟 is number of parallel cells
𝑛𝑠𝑒𝑟 is number of series cells
The value of 𝑛𝑠𝑒𝑟 is available from motor specification. From Eq. (4) the weight of the battery can be estimated
by multiplying a total number of cells and individual battery cell weight.
Where
𝑤𝑏𝑎𝑡 is total estimate battery weight (kg)
𝑛𝑡𝑜𝑡 is total number of cells
𝑤𝑐𝑒𝑙𝑙 is individual cell weight (kg)
𝑤𝑏𝑎𝑡 = 𝑛𝑡𝑜𝑡 ∙ 𝑤𝑐𝑒𝑙𝑙
060008-3
(6)
Calculating Propulsion Weight
The propulsion weight includes a battery, motor, and propeller. This will simply add the weight of motor,
ESC, and propeller and multiply by number or rotor. Then add the weight of the battery.
𝑊𝑝 = 𝑤𝑏𝑎𝑡 + 𝑛(𝑤𝑚𝑜𝑡 + 𝑤𝑒𝑠𝑐 + 𝑤𝑝𝑟𝑜𝑝 )
(7)
Where
𝑊𝑝
is the propulsion weight
𝑤𝑏𝑎𝑡 is the total weight of battery
𝑤𝑚𝑜𝑡 is the total weight of individual motor
𝑤𝑒𝑠𝑐 is the weight of individual ESC
𝑤𝑝𝑟𝑜𝑝 is the total weight of individual propeller
BUILDING THE TABLE
This table requires iterating calculation. First, we specify an array of take-off weight value. For every value,
calculate it by inserting take-off weight value into Eq. (2). Then insert motor current consumption from Eq. (2) into
Eq. (3), until we have the total weight of the propulsion system and battery 𝑊𝑝 from Eq. (7).
𝑊𝑎𝑓 = 𝑊𝑇𝑂 − 𝑊𝑝
(8)
Where
𝑊𝑎𝑓 is the available weight for airframe and payload
𝑊𝑇𝑂 is the total takeoff weight
𝑊𝑃 is the total weight propulsion system
With Eq. (9), we can calculate the remaining weight for airframe and payloads, including avionics. We need to
iterate this calculation for the next takeoff weight value, then do the same calculation for all available motors. This
calculation will be simpler when we use a spreadsheet.
Now, after we have the whole map of possible propulsion configuration, the last step is we need to make sure that
the combination has valid value and enough thrust to weight. Thrust to weight ratio is the comparison between the
maximum thrust of all propulsions and weight of the aircraft.9
𝑅𝑇𝑇𝑊 =
𝑇𝑚𝑎𝑥
𝑊𝑇𝑂
𝑇𝑚𝑎𝑥 = 𝑛 ∙ 𝑡𝑚𝑎𝑥
(9)
(10)
Where
𝑅𝑇𝑇𝑊 is thrust to weight ratio
𝑇𝑚𝑎𝑥 is total maximum thrust
𝑊𝑇𝑂 is takeoff weight
𝑛
is number of rotors
𝑡𝑚𝑎𝑥 is maximum thrust per rotor, from motor specification
Some calculations can have heavier propulsion system than the takeoff weight, resulting in negative airframe
weight. Some calculations also can result in heavier takeoff weight than the maximum thrust of the propulsion. Those
calculations need to be excluded and marked as impossible.
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Zone
Overpower
Safe
Critical
Impossible
TABLE 1. Zoning of the thrust table.
Meaning
Color
𝑅 > 𝑅𝑚𝑎𝑥
Yellow
𝑅𝑚𝑖𝑛 < 𝑅 ≤ 𝑅𝑚𝑎𝑥
Green
1 < 𝑅 ≤ 𝑅𝑚𝑖𝑛
Red
𝑅 ≤ 1 or 𝑊𝑃 > 𝑊𝑇𝑂
Grey
Therefore, we need to consider thrust to weight ratio. So, there will be 5 zones in the table as mentioned in table 1.
The first zone is where the thrust to weight ratio R less than 1 or the weight of the propulsion system 𝑊𝑃 is heavier
than specified take-off weight 𝑊𝑇𝑂 , which means the design is impossible. When the total weight of the aircraft
exceeds the maximum force of the propulsion system, the propulsion system is unable to lift the aircraft. The other
meaning of the impossible zone is when maximum take-off weight is below the weight of the propulsion system. That
means we need a negative weight to make design possible.
FIGURE 2. The thrust table in colored spreadsheet
The second zone is the safe zone where the design is possible. In that zone, the thrust to weight ratio R is between
specified thrust to weight minimum 𝑅𝑚𝑖𝑛 and thrust to weight maximum 𝑅𝑚𝑎𝑥 . Typically, thrust to weight ratio11 is
2, but it depends on the required maneuverability. The other zones are the overpower zone where the thrust is
considered too much and the critical zone where the thrust is doubtfully able to lift the aircraft. In the critical zone,
the propulsion system theoretically can lift the aircraft but doesn’t have sufficient power for maneuvering. All those
ratio limits are depending on the required maneuverability. In that case, those values may vary in each design.
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RESULT AND DISCUSSION
Several factors that have not been taken into consideration yet, such as price, propeller size, battery configuration,
and availability. Some motors could be not in stock or use a high voltage battery that requires high voltage ESCs.
Based on table 1, there are several options can satisfy our design requirement, marked with green cells in specific
takeoff weight column. The numbers on the cells are indicating the available weight for airframe and payload. We can
simply choose the largest number in the column if we do not consider another factor such as propeller size and cost.
The green area is the safe zone, as described in table 1, all the possible combinations that matched our requirement.
The yellow area marked thrust-to-weight ratio is in overpower zone. The red area is the critical zone and the grey area
marked the impossible zone because of negative available weight or thrust to weight ratio is less than 1. All the green
zone in a column are our options.
The next step we have to do is designing the airframe with a requirement of the weight less than a number in a
green cell including its payload. If the design of airframe is not satisfying the calculation, we need to look at another
takeoff weight column or another green cell.
Study Case
In our case, we need to design a multirotor capable to lift 5kg payload and a minimum of 20 minutes of flight time
for a delivery operation. The first thing we do is input 20 minutes of flight time, then choose our battery. For the
battery, we are using with lithium-ion NCR18650GA because of high density and readily available on the market.
Each NCR18650GA cell has 3.5Ah capacity and 48gram weight. We have no constraint for propeller size. We look
for green cells with a value of at least 5 kg. We discover that hexacopter is a better option for our case than a
quadcopter.
FIGURE 3. Options for our design
From the result in Fig. 4, we find out that T-Motor MN501s kv300 with 22” propeller is the best option. When we
design with 13kg maximum takeoff weight (MTOW), it can lift 8.53kg weight excluding propulsion and battery. With
calculation from Eq. (4), we need 6 series and 7 parallels of NCR18650GA. By removing 5kg from 8.53kg, we have
3.53kg for airframe and additional components. From that result, we know that the safe limit of the chosen
configuration is 18kg. The more MTOW, the more batteries need to be added for the same flight time. If we choose
14kg MTOW, we have 10.5kg for payload and airframe but we need 8 parallels of NCR18650GA. If we design with
MTOW above 18kg, the aircraft may not lift properly or difficult to maneuver once airborne.
CONCLUDING REMARKS AND FUTURE WORKS
From this experiment, we can conclude that our method is able to help make decisions easier by measuring motor
capability based on the table. This method can provide several options for the most optimum options from the available
propulsion system. For further work and improvement, the method can be combined with a thrust benchmark system
to collect actual motor data. Thrust benchmark system is a tool to obtain the propulsion model10 but this method only
needs thrust and current information from test bench. Another thing to note, this calculation currently uses the
assumption that multirotor is in hovering mode in the same air pressure as the test bench and does not include current
consumption when maneuvering.
ACKNOWLEDGEMENT
The author would like to acknowledge that this work was supported by PT Bukalapak.com.
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