MARKUS GASTENS Markus.firstname.lastname@example.org
The standard before the popularization of turbine engines, radial engines cylinder engines “radiate” out from the center through a reciprocating type of internal combustion. They dominated the skies for more than half a century due to their ability to self-air-cool and the sheer power they produced.
The first, water cooled, radial engine was constructed in 1901 by C. M. Manly and produced 52 BHP at 950 RPM. But it took almost a decade for the radial engine to be considered trustworthy for flying. Aluminum cylinders with steel liners were modified, providing radial engine’s reliability on long-range flights over water. The J-5 radial engine was even used for the first solo, trans-Atlantic flight. By WWII, radial engines had fully replaced rotary engines as the standard and provided much of the aircraft power. The demand for faster and higher flying eventually replaced them for jet engines. Radial engines are still in use in old aircrafts.
In radial engines all rods are connected to one master-rod, who is connected to the crankshaft. Therefore all forces act in the same plane which have to be synchronized to the crankshaft rotation angle to result a uniform, periodical output torque.
The idea of this project is to remodel this concept of engine, regarding to reference engines and compare the output power of the simulation and experimental investigations. The synchronization of the 5 piston forces to a nearly constant output torque stands in focus of this investigation.
This project presents the modelling and simulation of a 5-rod radial engine. The individual elements of the engine were digitized using the process of reverse engineering.
After modelling and assembly of the single parts with Autodesk Inventor, the assembly was imported into MSC Adams. The aim of this project is:
- To model this old engine concept capable to reach a stable state of rotation
- Reproduce realistic combustion forces and apply them to the system
- Determine the output torque and angular velocity of the motor in a dynamic state and compare them to reference engine values.
Mechanism description and kinematic chain
To understand the functioning of the radial engine, the different parts and their kinematic chain will be described.
In general the radial engine differs in two points to a common combustion engine:
- Cylinders are placed “radiate” out from the center outwards and not in one row-,V-, or boxer-configuration
- All cylinders are placed in one plane connected to only one crankshaft pin over a so called master-rod and not in different planes and pins of the crankshaft.
The geometry is based on the Verner Scarlet 5Si radial engine .
The pistons (gray) are positioned around the crankshaft-pin (green) in an angle of 360°/5=72° between each piston. They can only make a translational displacement towards and backwards the crank-pin-center, therefore every piston is constrained over a translational joint. Every piston is either connected to one of the four rods (red) or the one master-rod (blue) within a spherical joint. The master-rod consists of an rod fixed joined to two plates and four pins for the other rods. It has the function to forces on the crankshaft and to prevent a sliding of the plates around the crankshaft-pin. Every rod is connected to the master-rod over a cylindrical joint as well as the master-rod and the crankshaft (green). The crankshaft has a fixed connection to the propeller.
The crankshaft itself is connected over an revolute joint to the ground.
In the first step the geometry has been created and assembled recording to the Verner Scarlet 5Si in Autodesk Inventor. The according .step files were loaded into MSC Adams and material properties of steel were added, except of the propeller. It was assigned a moment of inertia of I=4200kg*cm^2 and a mass of m=5.44kg, based on the selected example of a typical propeller in for lightweight aircrafts .
After importing the geometry, constraints and forces were applied.
Joints and Constraints
The following connectors have been applied:
|Body 1||Body 2||Joint|
|Master-rod||4 x Rods||Cylindrical|
|4 x Rods||4 x Pistons||Spherical|
Gruebler-Count: 6×12(Parts) – 6×1(Fix) – 5×1(Rev) – 4×5(Cyl) – 3×5(Sph) –
5×5(Trans) = 1 DOF
There are no redundant constraint and the system is able to rotate around its crankshaft axis, to drive the propeller.
To avoid over-constraining of the system only constraints in form of single-point-forces on the pistons and torque around the crankshaft are applied.
Synchronization of forces
The challenge in this project was the synchronization of applied forces to the effective crank-angle which took the most of the time. To do so a measurement of the angle around the crankshaft over time has been created. It indicates the current position of the crank. Due to a rotation counterclockwise, values are negative but a sign correction has been performed.
That current position is connected to the current force value over a spline function. That means that for every piston has his own spline, where the force is applied as soon as the crank-angle corresponds to the upper cylinder position. For this purpose Akima function, type AKISPL was used. The AKISPL function uses Akima spline interpolation to return the y values for the x variable input through the spline entity. It uses spline curve in x–y direction . A full cycle of applying force takes normally 90° .
For example if piston 1 has his deadpoint on 0° the Spline function will give back recent values for the current angle (see figure) for the 90° of combustion. The force of piston 2 will be shifted for 72°, regarding piston 1, piston 3 for 144°, and so on. With this method a 360° cycle with every 72° piston combustion, piston per piston, can be modelled.
The peak forces are based on a 9.65 MPa firing pressure, which results with a bore of 70mm diameter to F_peak=37.1kN 
Normally an engine cycle includes 720° (360° for inlet and compression + 360° for combustion and outlet) which could not been modelled in this project and held open as an option to improve the model for further work.
Application of a breaking-torque
To drive the propeller in a steady state, a steady angular velocity has to be reached. Within a steady angular velocity there comes a steady torque on the crankshaft. This torque can be changed be increased by increasing the force on the pistons: increase gasoline injection –> increase of combustion pressure –> increase of force on piston –> increase of engine-torque
To reach a steady state, the engine needs a breaking-torque which stops the motor from accelerating. Normally this breaking-torque equals the torque which is transformed into energy to accelerate the air over the propeller and is controlled by the amount of gasoline injected. Though the simulation should be in a state of constant force peaks and the aerodynamic drag forces of the propeller are unknown, the applied breaking-torque equals the torque which is needed to accelerate the propeller.
To do so, the average torque when reaching the desired angular velocity has been measured and applied on the crankshaft in counter direction of the rotation. It is applied as soon as the acceleration to the target angular velocity is ended. After that, the system stays in a constant state.
The dynamic simulation was performed for a duration of 10 sec and a step size of 0.0001 in order to be able to accurately reproduce the short-term application of force.
After a short period of acceleration of 0.18 sec the system reaches the desired angular velocity of 2400RPM = 14400 deg/sec (typical value for take-off ) and the breaking-torque is applied (see figure below). With applied breaking-torque, the system rotates in a steady state.
The figure below shows the applied force on the pistons over the time of approximately two and a half cycles after reaching the steady state. The pistons seem to fire uniform one after another, like it is supposed to be. The forces follow the implemented spline function and reach the desired peak force of 37.1 kN. Due to the counterclockwise direction of rotation the pistons firing from piston 5 down to piston 1.
The measurement of the piston position shows that the pistons move periodical and with a uniform phase shift between every piston. The different amplitude results from different angle of assembly towards the master-rod, which is represented through the piston number 1. The piston 1 position amplitude of 30mm equals the cranklength of the crankshaft.
Below there is the measurement of the torque around the crankshaft axis which leads to the propeller. We can see that the torque is cycling quiet uniform around an average value of T_avg= 5.7E+05 Nmm. This combined with the angular velocity leads to the proper output power of the estimated model P = 2*PI*T_avg*n = 2*PI*5.7E+05 Nmm * 2400 RPM /60=144.277 kW = 193 HP with fits to a comparable engine with a 148 kW at 2400 RPM from NASA investigations on radial engines .
The slightly different amplitudes of the torque can be explained by the slightly different stroke of every rod.
The goal to remodel the engine concept was successful and leaded to a similar torque output compared to investigated radial engines by NASA.
It was possible to couple the piston forces to the actual crankshaft angle by connecting them over a spline function. Therefore the engine can reach a steady mode with applied counter torque, avoiding an endless acceleration of the model.
After reaching the steady state, the system is cycling around this state and does not change it’s behavior.
Therefore the aims of the project have been achieved.
 Bialy, Michal: Crank-piston model of internal combustion engine using CAD/CAM/CAE in the MSC Adams
 NASA Contractor Report 3260: 150 and 300 kW Lightweight Diesel Aircraft Engine Design Study
 Radial Engine Verner Scarlett 5Si: http://scalebirds.com/scarlett-5
 Schreiner, Klaus: Basiswissen Verbrennungsmotor
 Stearman, Paul: Radial engine from a Boing Foto
 Vivian, E. Charles (1920): A History of Aeronautics