## 1 Introduction  
Since the research on the buckling load of thin-walled cylinders began in 1947 [1], this topic has been studied for 60 years. However, we still do not know the effect of the scatter and deviation of the buckling load between theory and experiment. [PERSON] measured shape imperfections in cylinders and found that a nonlinear finite element analysis gave results that were 5-10% larger than the experimental buckling loads [2]. It is necessary to measure the shape imperfections using this method before production; however, this method cannot be used for prediction. [PERSON] employed FEM to investigate the probabilistic design of axially compressed composite cylinders with geometric and loading imperfections but did not explore the relationship between KDF and shape imperfections [3]. [PERSON] investigated the influence of cylinder length (\(L\)) on KDF [4]. [PERSON] investigated the effect of \(r/t\) and \(L/r\) on KDF using FEM [5]. [PERSON] conducted buckling analysis of thin-walled cylinder structures and structural improvements using FEM [6]. [PERSON] investigated the buckling of cylinders with cutouts under axial compression [7].  
Most of the research on buckling of thin-walled cylinders has focused on FEM, with relatively few physical experiments conducted. This paper summarizes previous physical experiments and adds a significant number of experiments conducted by the authors to explore the buckling strength of CFRP cylinders. Through this, we hope to discover some patterns. There have been many investigations on the buckling load of thin-walled cylinders made from carbon fiber-reinforced plastic (CFRP) [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22], the results of which are summarized in [23].  
The buckling tests in these previous studies were conducted on cylinders with radius-thickness ratios up to \(r/t\) (radius-thickness ratio) = 893, and the relationship between buckling load and the knockdown factor (KDF = experimental value/theoretical value) was investigated [24]. Figure 1 summarizes the KDFs of thin-walled cylinders determined therein. Note that only two \(r/t\) = 893 data were obtained; thus, more tests will be required to make conclusions on those data.  
Regression analyses further showed that various factors, including layup overlaps or gaps, the \(r/t\), the \(L/r\) (length-radius ratio), layup stiffness, and oval shape imperfection, are not statistically significant [25].  
Buckling tests with the cylinders under the offset between the center of the compression load and the center of the cylinder showed that the decrease in KDF is not directly correlated to the offset or amplitude of local directional-shape imperfections [24]. Still, since the offsets of \(0^{\circ}\), \(90^{\circ}\), \(180^{\circ}\), and \(270^{\circ}\) did not correspond to the maximum (or minimum) amplitudes of the local shape imperfections, more tests need to be conducted to confirm these findings.  
Furthermore, it was found that the KDF decreases when the amplitude of pentagonal imperfections increases. But when this information was added to the other data and analyzed, the tendency for the KDF to decrease when the amplitude of pentagonal imperfections increased disappeared. The reason for the disappearance of this tendency is suspected to be that the KDF is a normalized value, whereas the amplitude of shape imperfections is not normalized. Hence, in the study reported below, the relationship between the KDF and out-plane shape imperfections normalized by the wall thickness  
Figure 1: KDF values of CFRP thin-walled cylinders for a large range of \(r/t\)[24].  
was investigated. Nine CFRP cylindrical specimens with different wall thicknesses were made and tested to examine the relationship between the KDF and normalized out-plane shape imperfections.