Help with Snake like movement algorithm.

Hi all!

i'm trying to create snake like movement that act more like cars convoy then a snake. below the code i came with. it works well as snake but i can't figure out how to keep distance between body parts and keep the movement smooth (like car movement):

this part create a "hidden" snake and take care of controlling it.

 using UnityEngine;
 using System.Collections;
 using System.Collections.Generic;
 
 public class MovementController : MonoBehaviour {
 
     public int ConvoyLength=3;
     public GameObject HeadObj;
     public GameObject SpacerObj;
     public GameObject temp;
     public static List<Member> Convoy = new List<Member>();
     private Vector3 pos;
     private float Speed = 10f;
     private float xDir;
     private float zDir;
 
     private int direction=4;
     private float timer;
     public float deltaTimer=1f;
 
     // Use this for initialization
     void Start () {
         xDir=Speed;
         HeadObj= Resources.Load ("Prefabs/test/Body") as GameObject;
         SpacerObj= Resources.Load ("Prefabs/test/Spacer") as GameObject;
 
         //Convoy.Add (HeadObj);
         if(ConvoyLength>1){
             Debug.Log ("adding more body");
             AddConvoyMembers();
         }
         pos= new Vector3(0f,0f,0f);
     
 
     
     }
     
     // Update is called once per frame
     void Update () {
         timer+=Time.deltaTime;
         //Convoy[0].transform.position=pos;
         if(Input.GetKey(KeyCode.UpArrow) ){
             xDir= 0f;
             zDir=Speed;
             direction= 1;
         }
         if(Input.GetKey(KeyCode.DownArrow) ){
             xDir= 0f;
             zDir= -Speed;
             direction=3;
         }
         if(Input.GetKey(KeyCode.LeftArrow) ){
             xDir= -Speed;
             zDir= 0f;
             direction=2;
         }
         if(Input.GetKey(KeyCode.RightArrow) ){
             xDir= Speed;
             zDir= 0f;
             direction=4;
         }
 //        if(Input.GetKeyDown(KeyCode.Space) ){
 //            ConvoyLength+=1;
 //            Convoy.Add (BodyObj);
 //            Convoy[ConvoyLength]= Instantiate (BodyObj,pos,Quaternion.identity) as GameObject;        
 //        }
 
 
         //Convoy[0].posX = Convoy[0].posX + xDir* Time.deltaTime;
         //Convoy[0].posZ = Convoy[0].posZ + zDir* Time.deltaTime;
         if(timer > deltaTimer){
             Convoy[0].posX = Convoy[0].posX + xDir* Time.deltaTime;
             Convoy[0].posZ = Convoy[0].posZ + zDir* Time.deltaTime;
             Convoy[0].Dir = direction;
             MoveConvoy();    
             timer-=deltaTimer;
         }
     }
 
     void AddConvoyMembers(){
         float tempPos=0;
         Vector3 tempPos2 = new Vector3(tempPos,0f,0f);
         for(int i=0;i<ConvoyLength;i++ ){
             Convoy.Add (new Member());
         }
 
 
         temp = Instantiate (SpacerObj,tempPos2,Quaternion.identity) as GameObject;
         temp.tag="0";
         for(int i=1;i<ConvoyLength;i++ ){
             Convoy[i] = new Member();
             //Convoy[i].posX = tempPos;
             if(i%2==0){temp = Instantiate (HeadObj,tempPos2,Quaternion.identity) as GameObject;
             temp.tag=i.ToString ();
             }
         }
     }
     void MoveConvoy(){
         for(int index=ConvoyLength-1;index>0;index--){
 
                 Convoy[index].posX = Convoy[index-1].posX;
                 Convoy[index].posZ = Convoy[index-1].posZ;
                 Convoy[index].Dir = Convoy[index-1].Dir;
             
         }
         
         
     }

then i have this code for the body parts, the idea that when i spawn new part with specific tag number it snap to it place on the hidden snake. it also make sure it rotate nicely to the current direction.

 using UnityEngine;
 using System.Collections;
 
 public class MemberController : MonoBehaviour {
     private int TagNumber;
     private GameObject nextMember;
     private Vector3 pos;
     public float TurnSpeed;
     // Use this for initialization
     void Start () {
         TagNumber= int.Parse(this.tag);
         //this.transform.position=MovementController.Convoy[TagNumber].transform.position;
         }
        
     // Update is called once per frame
     void Update () {
         pos= new Vector3(MovementController.Convoy[TagNumber].posX,0f,MovementController.Convoy[TagNumber].posZ);
         this.transform.position= Vector3.Lerp (this.transform.position,pos,TurnSpeed* Time.deltaTime) ;
         //this.transform.position= pos;
         if(MovementController.Convoy[TagNumber].Dir==2){
             Quaternion target = Quaternion.Euler(0, 180f, 0f);
             transform.rotation = Quaternion.Slerp(transform.rotation, target, TurnSpeed * Time.deltaTime);
         }
         if(MovementController.Convoy[TagNumber].Dir==4){
             Quaternion target = Quaternion.Euler(0, 0f, 0f);
             transform.rotation = Quaternion.Slerp(transform.rotation, target, TurnSpeed *Time.deltaTime);
             
         }
         if(MovementController.Convoy[TagNumber].Dir==1){
             Quaternion target = Quaternion.Euler(0, -90f, 0f);
             transform.rotation = Quaternion.Slerp(transform.rotation, target, TurnSpeed *Time.deltaTime);
             
         }
         if(MovementController.Convoy[TagNumber].Dir==3){
             Quaternion target = Quaternion.Euler(0, 90f, 0f);
             transform.rotation = Quaternion.Slerp(transform.rotation, target, TurnSpeed *Time.deltaTime);
             
         }
         //this.transform.position=MovementController.Convoy[TagNumber].transform.position;
     }
 }

and this public class for the body hidden parts:

 public class Member{
     public float posX{ get; set;}
     public float posZ{ get; set;}
     public int Dir{ get; set;}
 }

that's it. not very complected. in the main script i have the variable "Speed" if i set it to high number i do get gaps between parts but the snake moves too fast for my needs. i tried to implement timing to slow it down but then it create jumpy movement.

i'm open to your suggestions...

thanks!!